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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

Fernandes, Henrique Almeida
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
Relevância na Pesquisa
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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...

## 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

Silveira, Marcilei Aparecida Guazzelli da
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
Relevância na Pesquisa
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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...

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

Felmer Aichele, Patricio L.; Quaas, Alexander; Esteban, María J.
Tipo: Artículo de revista
EN
Relevância na Pesquisa
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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.

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

Antonenko, S. A.; Sokolov, A. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.66237%
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

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

Kaupuzs, J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.58339%
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...

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

Cavalcante, Hugo L. D. de S.; Leite, J. R. Rios
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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)

## Critical Exponents of the Random Field Hierarchical Model

Parisi, Giorgio; Rocchi, Jacopo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.58339%
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

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

Ramirez-Santiago, G.; José, Jorge V.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.718047%
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)

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

Codello, A.; Defenu, N.; D'Odorico, G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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

## Critical exponents of colloid particles in bulk and confinement

Neitsch, Helge; Klapp, Sabine H. L.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.71941%
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...

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

Ivanytskyi, A. I.; Bugaev, K. A.; Sorin, A. S.; Zinovjev, G. M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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...

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

Choo, C. H.; Schriemer, H. P.; Taylor, D. R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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

## Critical Exponents from AdS/CFT with Flavor

Karch, Andreas; O'Bannon, Andy; Yaffe, Laurence G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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...

## Critical exponents of the anisotropic Bak-Sneppen model

Maslov, Sergei; Rios, Paolo De Los; Marsili, Matteo; Zhang, Yi-Cheng
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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

## Critical exponents in zero dimensions

Alexakis, Alexandros; Pétrélis, François
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.610703%
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.

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

Kaupuzs, J.
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...

## Surface critical exponents at a uniaxial Lifshitz point

Pleimling, Michel
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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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

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

Feldman, D. E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.58339%
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

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

Mo, Jie-Xiong; Liu, Wen-Biao
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.58339%
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...

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

Carlon, Enrico; Igloi, Ferenc
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