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## Propriedades críticas estáticas e dinâmicas de modelos com simetria contínua e do modelo Z(5); Static and dynamic critical properties of models with continuous symmetry and of the Z(5) model

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 04/08/2006
PT

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#classe de universalidade#critical exponents#critical phenomena.#dinâmica crítica de tempos curtos#expoentes críticos#fenômenos críticos.#Monte Carlo simulations#short-time critical dynamics#Simulações Monte Carlo#universality class

Neste trabalho, nós investigamos o comportamento crítico dinâmico de três modelos estatísticos utilizando simulações Monte Carlo em tempos curtos. Inicialmente, estudamos os modelos tridimensionais de dupla-troca e de Heisenberg. O expoente dinâmico de persistência global, bem como o expoente z são estimados através de duas técnicas. Para obter o expoente de persistência global, aplicamos diretamente a lei de potência obtida para a probabilidade de persistência global e em seguida fizemos o colapso de uma função universal para duas redes de tamanhos diferentes. Para estimar o valor de z, nós usamos uma função mista que combina resultados de simulações realizadas com diferentes condições iniciais e o cumulante de Binder de quarta ordem dependente do tempo. O expoente dinâmico que governa o comportamento tipo lei de potência da magnetização inicial, é estimado através da correlação temporal da magnetização (modelos de dupla-troca e Heisenberg) e da aplicação direta de uma lei de potência (modelo de Heisenberg). Os expoentes estáticos da magnetização e comprimento de correlação são estimados seguindo o comportamento de escala do parâmetro de ordem e sua derivada, respectivamente. Os resultados confirmam que esses dois modelos pertencem à mesma classe de universalidade. Em seguida...

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## Medidas de expoentes críticos de filmes de diamante por meio de microscopia de força atômica; Measures of critical exponents of diamond films using atomic force microscopy

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 28/05/1999
PT

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#Atomic force microscopy#Critical exponents#Diamond films#Expoentes críticos#Filmes de diamante#KPZ#KPZ#Leis de escala#Microscopia de força atômica#Scale laws

Neste trabalho investigamos a dinâmica de crescimento de filmes de diamante sintetizados por meio de deposição química a vapor ativada por plasma de microondas (CVD). A caracterização foi feita utilizando, fundamentalmente, microscopia de força atômica (AFM). Analisamos o comportamento da rugosidade dos filmes como função da escala de observação e do tempo de deposição. Dessa maneira verificamos a existência de leis de potência para o crescimento e determinamos os expoentes críticos associados a essas leis. Os resultados obtidos estão em bom acordo com o processo de crescimento descrito pela equação estocástica KPZ. Os mecanismos principais são a deposição aleatória de partículas na superfície, o crescimento lateral e a dessorção.; Diamond films have been grown by Microwave Plasma assisted Chemical Vapor Deposition (CVD). The characterization has been made mainly by Atomic Force Microscopy (AFM). We could analyze the roughness behavior with the scale of observation and with the deposition time. We could determine the critical exponents associated with these laws. The results suggest that the growth process is in good agreement with the stochastic growth equation known as KPZ. The most important mechanisms are the random deposition...

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## Large critical exponents for some second order uniformly elliptic operators

Fonte: Universidade do Chile
Publicador: Universidade do Chile

Tipo: Artículo de revista

EN

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Publicación ISI; In this paper we investigate the critical exponents of two families of Pucci's extremal operators. The notion of critical exponent that we have chosen for these fully nonlinear operators which are not variational is that of threshold between existence and nonexistence of the solutions for semilinear equations with pure power nonlinearities. Interesting new exponents appear in this context.

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## Critical exponents for 3D O(n)-symmetric model with n > 3

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/03/1998

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#High Energy Physics - Theory#Condensed Matter#High Energy Physics - Lattice#High Energy Physics - Phenomenology

Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated
on the base of six-loop renormalization-group (RG) expansions. A simple
Pade-Borel technique is used for the resummation of the RG series and the Pade
approximants [L/1] are shown to give rather good numerical results for all
calculated quantities. For large n, the fixed point location g_c and the
critical exponents are also determined directly from six-loop expansions
without addressing the resummation procedure. An analysis of the numbers
obtained shows that resummation becomes unnecessary when n exceeds 28 provided
an accuracy of about 0.01 is adopted as satisfactory for g_c and critical
exponents. Further, results of the calculations performed are used to estimate
the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to
play the role of the lower boundary of the domain where this approximation
provides high-precision estimates for the critical exponents.; Comment: 10 pages, TeX, no figures

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## Transfer matrix and Monte Carlo tests of critical exponents in lattice models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The corrections to finite-size scaling in the critical two-point correlation
function G(r) of 2D Ising model on a square lattice have been studied
numerically by means of exact transfer-matrix algorithms. The systems of square
geometry with periodic boundaries oriented either along <10> or along <11>
direction have been considered, including up to 800 spins. The calculation of
G(r) at a distance r equal to the half of the system size L shows the existence
of an amplitude correction proportional to 1/L^2. A nontrivial correction
proportional to 1/L^0.25 of a very small magnitude also has been detected in
agreement with predictions of our recently developed GFD (grouping of Feynman
diagrams) theory. A refined analysis of the recent MC data for 3D Ising, phi^4,
and XY lattice models has been performed. It includes an analysis of the
partition function zeros of 3D Ising model, an estimation of the
correction-to-scaling exponent omega from the Binder cumulant data near
criticality, as well as a study of the effective critical exponent eta and the
effective amplitudes in the asymptotic expansion of susceptibility at the
critical point. In all cases a refined analysis is consistent with our (GFD)
asymptotic values of the critical exponents (nu=2/3...

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## Averages and Critical Exponents in Type-III Intermittent Chaos

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/03/2003

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The natural measure in a map with type-III intermittent chaos is used to
define critical exponents for the average of a variable from a dynamical system
near bifurcation. Numerical experiments were done with maps and verify the
analytical predictions. Physical experiments to test the usefulness of such
exponents to characterize the nonlinearity at bifurcations were done in a
driven electronic circuit with diode as nonlinear element. Two critical
exponents were measured: $\nu = 0.55$ for the critical exponent of the average
of the voltage across the diode and $\beta = 0.62$ for the exponent of the
average length of the laminar phases. Both values are consistent with the
predictions of a type-III intermittency of cubic nonlinearity. The averages of
variables in intermittent chaotic systems is a technique complementary to the
measurements of laminar phase histograms, to identify the nonlinear mechanisms.
The averages exponents may have a broad application in ultrafast chaotic
phenomena.; Comment: 5 pages, 7 figures, published. Journal ref: Physical Review E, 66,
026210 (2002)

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## Critical Exponents of the Random Field Hierarchical Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/09/2013

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We have studied the one dimensional Dyson hierarchical model in presence of a
random field. This is a long range model where the interactions scale with the
distance with a power law-like form J(r) ~ r^{-\rho} and we can explore mean
field and non-mean field behavior by changing \rho. Thus, it can be used to
approach the phase transitions in finite-dimensional disordered models. We
studied the model at T=0 and we numerically computed its critical exponents in
the non-mean field region for Gaussian disorder. We then computed an analytic
expression for the critical exponent \delta, that holds in the non-mean field
region, and we noted an interesting relation between the critical exponents of
the disordered model and the ones of the pure model, that seems to break down
in the non-mean field region. We finally compare our results for the critical
exponents with the expected ones in D-dimensional short range models and with
the ones of the straightforward one dimensional long range model.; Comment: 9 pages, 3 figures

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## Critical Exponents of the Fully Frustrated 2-D Xy Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/02/1994

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We present a detailed study of the critical properties of the 2-D XY model
with maximal frustration in a square lattice. We use extensive Monte Carlo
simulations to study the thermodynamics of the spin and chiral degrees of
freedom, concentrating on their correlation functions. The gauge invariant
spin-spin correlation functions are calculated close to the critical point for
lattice sizes up to $240\times 240$; the chiral correlation functions are
studied on lattices up to $96\times 96$. We find that the critical exponents of
the spin phase transition are $\nu=0.3069$, and $\eta=0.1915$, which are to be
compared with the unfrustrated XY model exponents $\nu=1/2$ and $\eta=0.25$. We
also find that the critical exponents of the chiral transition are
$\nu_{\chi}=0.875$, $2\beta=0.1936$, $2\gamma= 1.82$, and
$2\gamma\>\prime=1.025$, which are different from the expected 2-D Ising
critical exponents. The spin-phase transition occurs at $T_{U(1)}=0.446$ which
is about 7\% above the estimated chiral critical temperature $T_{Z_{2}}=
0.4206$. However, because of the size of the statistical errors, it is
difficult to decide with certainty whether the transitions occur at the same or
at slightly different temperatures. Finally, the jump in the helicity modulus
in the fully frustrated system is found to be about 23\% below the unfrustrated
universal value. The most important consequence of these results is that the
fully frustrated XY model appears to be in a novel universality class. Recent
successful comparisons of some of these results with experimental data are also
briefly discussed. (TO APPEAR IN PRB); Comment: 47 pages (PHYZZX)

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## Critical exponents of O(N) models in fractional dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We compute critical exponents of O(N) models in fractal dimensions between
two and four, and for continuos values of the number of field components N, in
this way completing the RG classification of universality classes for these
models. In d=2 the N-dependence of the correlation length critical exponent
gives us the last piece of information needed to establish a RG derivation of
the Mermin-Wagner theorem. We also report critical exponents for multi-critical
universality classes in the cases N>1 and N=0. Finally, in the large-N limit
our critical exponents correctly approach those of the spherical model,
allowing us to set N~100 as threshold for the quantitative validity of leading
order large-N estimates.; Comment: 6 pages, 5 figures, reference added

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## Critical exponents of colloid particles in bulk and confinement

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/11/2012

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Using grand canonical Monte Carlo simulations, we investigate the percolation
behavior of a square well fluid with an ultra-short range of attraction in
three dimension (3D) and in confined geometry. The latter is defined through
two parallel and structureless walls (slit-pore). We focus on temperatures
above the critical temperature of the (metastable) condensation transition of
the 3D system. Investigating a broad range of systems sizes, we first determine
the percolation thresholds, i. e., the critical packing fraction for
percolation $\eta_{c}$. For the slit-pore systems, $\eta_{c}$ is found to vary
with the wall separation $L_{z}$ in a continuous but non-monotonic way,
$\eta_{c}(L_{z}\rightarrow\infty)=\eta_{c}^{\text{3D}}$. We also report results
for critical exponents of the percolation transition, specifically, the
exponent $\nu$ of the correlation length $\xi$ and the two fisher exponents
$\tau$ and $\sigma$ of the cluster-size distribution. These exponents are
obtained from a finite-size analysis involving the cluster-size distribution
and the radii of gyration distribution at the percolation threshold. Within the
accuracy of our simulations, the values of the critical exponents of our 3D
system are comparable to those of 3D random percolation theory. For narrow
slit-pores...

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## Critical exponents of the quark-gluon bags model with the critical endpoint

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/11/2012

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The critical indices \alpha', \beta, \gamma' and \delta of the Quark Gluon
Bags with Surface Tension Model that has the critical endpoint are calculated
and compared with the exponents of other models. These indices are expressed in
terms of the most general parameters of the model. Despite the usual
expectations the found critical indices do not depend on the Fisher exponent
\tau and on the parameter \varkappa which relates the mean bag surface to its
volume. The scaling relations for the obtained critical exponents are verified
and it is demonstrated that for the standard definition of the index \alpha'
the Fisher and the Griffiths scaling inequalities are not fulfilled in general
case, whereas the Liberman scaling inequality is always obeyed. This is not
surprising for the phase diagram with the asymmetric properties of pure phases,
but the present model also provides us with the first and explicit example that
the specially defined index \alpha'_s does not recover the scaling relations as
well. Therefore, here we suggest the physically motivated definition of the
index \alpha' = \alpha'_c and demonstrate that such a definition recovers the
Fisher scaling inequality, while it is shown that the Griffiths inequality
should be generalized for the phase diagram with the asymmetric properties. The
critical exponents of several systems that belong to different universality
classes are successfully described by the parameters of the present model and
hence its equation of state can be used for a variety of practical
applications.; Comment: Accepted for publication in PRE...

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## Crossover from classical to random-field critical exponents in As-doped TbVO4

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/02/2000

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Using birefringence techniques we have measured the critical exponents beta,
gamma, and delta in As-doped TbVO4, a structural realization of the
random-field Ising model where random strain fields are introduced by V-As size
mismatch. For pure TbVO4 we observe the expected classical critical exponents,
while for a mixed sample with 15% As concentration our results are beta=0.31
+/-0.03, gamma=1.22 +/-0.07, and delta=4.2 +/-0.7. These values are consistent
with the critical exponents for the short range pure Ising model in three
dimensions in agreement with a prediction by Toh. The susceptibility data
showed a crossover with temperature from classical to random field critical
behaviour.; Comment: 7 pages including 4 figures; To be published in Physical Review B

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## Critical Exponents from AdS/CFT with Flavor

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We use the AdS/CFT correspondence to study the thermodynamics of massive N=2
supersymmetric hypermultiplet flavor fields coupled to N=4 supersymmetric
SU(Nc) Yang-Mills theory, formulated on curved four-manifolds, in the limits of
large Nc and large 't Hooft coupling. The gravitational duals are probe
D-branes in global thermal AdS. These D-branes may undergo a topology-changing
transition in the bulk. The D-brane embeddings near the point of the topology
change exhibit a scaling symmetry. The associated scaling exponents can be
either real- or complex-valued. Which regime applies depends on the
dimensionality of a collapsing submanifold in the critical embedding. When the
scaling exponents are complex-valued, a first-order transition associated with
the flavor fields appears in the dual field theory. Real scaling exponents are
expected to be associated with a continuous transition in the dual field
theory. For one example with real exponents, the D7-brane, we study the
transition in detail. We find two field theory observables that diverge at the
critical point, and we compute the associated critical exponents. We also
present analytic and numerical evidence that the transition expresses itself in
the meson spectrum as a non-analyticity at the critical point. We argue that
the transition we study is a true phase transition only when the 't Hooft
coupling is strictly infinite.; Comment: 31 pages...

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## Critical exponents of the anisotropic Bak-Sneppen model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We analyze the behavior of spatially anisotropic Bak-Sneppen model. We
demonstrate that a nontrivial relation between critical exponents tau and
mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its
anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model
we derive a novel exact equation for the distribution of avalanche spatial
sizes, and extract the value gamma=2 for one of the critical exponents of the
model. Other critical exponents are then determined from previously known
exponent relations. Our results are in excellent agreement with Monte Carlo
simulations of the model as well as with direct numerical integration of the
new equation.; Comment: 8 pages, three figures included with psfig, some rewriting, + extra
figure and table of exponents

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## Critical exponents in zero dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/07/2012

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#Condensed Matter - Statistical Mechanics#Nonlinear Sciences - Chaotic Dynamics#Physics - Fluid Dynamics

In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents $\beta_m$ for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment.

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## Monte Carlo test of critical exponents in 3D Heisenberg and Ising models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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We have tested the theoretical values of critical exponents, predicted for
the three--dimensional Heisenberg model, based on the published Monte Carlo
(MC) simulation data for the susceptibility. Two different sets of the critical
exponents have been considered - one provided by the usual (perturbative)
renormalization group (RG) theory, and another predicted by grouping of Feynman
diagrams in phi^4 model (our theory). The test consists of two steps. First we
determine the critical coupling by fitting the MC data to the theoretical
expression, including both confluent and analytical corrections to scaling, the
values of critical exponents being taken from theory. Then we use the obtained
value of critical coupling to test the agreement between theory and MC data at
criticality. As a result, we have found that predictions of our theory
(gamma=19/14, eta=1/10, omega=3/5) are consistent, whereas those of the
perturbative RG theory (gamma=1.3895, eta=0.0355, omega=0.782) are inconsistent
with the MC data. The seemable agreement between the RG prediction for eta and
MC results at criticality, reported in literature, appears due to slightly
overestimated value of the critical coupling. Estimation of critical exponents
of 3D Ising model from complex zeroth of the partition function is discussed. A
refined analysis yields the best estimate 1/nu=1.518. We conclude that the
recent MC data can be completely explained within our theory (providing
1/nu=1.5 and omega=0.5) rather than within the conventional RG theory.; Comment: 16 pages...

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## Surface critical exponents at a uniaxial Lifshitz point

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/11/2001

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Using Monte Carlo techniques, the surface critical behaviour of
three-dimensional semi-infinite ANNNI models with different surface
orientations with respect to the axis of competing interactions is
investigated. Special attention is thereby paid to the surface criticality at
the bulk uniaxial Lifshitz point encountered in this model. The presented Monte
Carlo results show that the mean-field description of semi-infinite ANNNI
models is qualitatively correct. Lifshitz point surface critical exponents at
the ordinary transition are found to depend on the surface orientation. At the
special transition point, however, no clear dependency of the critical
exponents on the surface orientation is revealed. The values of the surface
critical exponents presented in this study are the first estimates available
beyond mean-field theory.; Comment: 10 pages, 7 figures included

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## Critical exponents of the random-field O(N) model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/10/2000

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The critical behavior of the random-field Ising model has been a puzzle for a
long time. Different theoretical methods predict that the critical exponents of
the random-field ferromagnet in D dimensions are the same as in the pure
(D-2)-dimensional ferromagnet with the same number of the magnetization
components. This result contradicts the experiments and simulations. We
calculate the critical exponents of the random-field O(N) model with the
(4+\epsilon)-expansion and obtain values different from the critical exponents
of the pure ferromagnet in 2+\epsilon dimensions. In contrast to the previous
approaches we take into account an infinite set of relevant operators emerging
in the problem. We demonstrate how these previously missed relevant operators
lead to the breakdown of the (6-\epsilon)-expansion for the random-field Ising
model.; Comment: 5 pages

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## Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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We investigate the phase transitions of black holes with conformal anomaly in
canonical ensemble from different perspectives. Some interesting and novel
phase transition phenomena have been discovered. Firstly, we discuss the
behavior of the specific heat and the inverse of the isothermal
compressibility. It is shown that there are striking differences in Hawking
temperature and phase structure between black holes with conformal anomaly and
those without it. In the case with conformal anomaly, there exists local
minimum temperature corresponding to the phase transition point. Phase
transitions take place not only from an unstable large black hole to a locally
stable medium black hole but also from an unstable medium black hole to a
locally stable small black hole. Secondly, we probe in details the dependence
of phase transitions on the choice of parameters. The results show that black
holes with conformal anomaly have much richer phase structure than those
without it. There would be two, only one or no phase transition points
depending on the parameters we have chosen. The corresponding parameter region
are derived both numerically and graphically. Thirdly, geometrothermodynamics
are built up to examine the phase structure we have discovered. It is shown
that Legendre invariant thermodynamic scalar curvature diverges exactly where
the specific heat diverges. Furthermore...

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## Density Profiles, Casimir Amplitudes and Critical Exponents in the Two Dimensional Potts Model: A Density Matrix Renormalization Study

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/10/1997

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We use the density matrix renormalization group (DMRG) to perform a detailed
study of the critical properties of the two dimensional Q state Potts model,
including the magnetization and energy-density profiles, bulk and surface
critical exponents and the Casimir amplitudes. We apply symmetry breaking
boundary conditions to a $L \times \infty$ strip and diagonalize the
corresponding transfer matrix for a series of moderately large systems ($L \le
64$) by the DMRG method. The numerically very accurate finite lattice results
are then extrapolated by efficient sequence extrapolation techniques. The
critical density profiles and the Casimir amplitudes are found to follow
precisely the conformal predictions for Q=2 and 3. Similarly, the bulk and
surface critical exponents of the models are in very good agreement with the
conformal and exact values: their accuracy has reached or even exceeded the
accuracy of other available numerical methods. For the Q=4 model both the
profiles and the critical exponents show strong logarithmic corrections, which
are also studied.; Comment: 12 pages, RevTeX, 14 PostScript figures included

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