Search results for " exponent"
showing 10 items of 315 documents
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
2001
Abstract A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one c…
Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model
1995
We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.…
Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
1994
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.
Monte Carlo study of surface phase transitions in the three-dimensional Ising model.
1990
We present the results of extensive Monte Carlo simulations of phase transitions and critical behavior at the surface of a simple cubic Ising model. Profiles of the magnetization and internal energy are determined as a function of the distance from the surface, and we extract surface and bulk properties as a function of temperature and surface coupling ${\mathit{J}}_{\mathit{s}}$. The surface-bulk multicritical point is located with improved precision, ${\mathit{J}}_{\mathit{s}}$/J=1.52\ifmmode\pm\else\textpm\fi{}0.02, and crossover behavior is studied. New estimates for critical exponents are extracted, ${\ensuremath{\gamma}}_{1}$=0.78\ifmmode\pm\else\textpm\fi{}0.06, ${\ensuremath{\gamma}…
Surface effects on phase transitions of modulated phases and at Lifshitz points: A mean field theory of the ANNNI model
1999
The semi-infinite axial next nearest neighbor Ising (ANNNI) model in the disordered phase is treated within the molecular field approximation, as a prototype case for surface effects in systems undergoing transitions to both ferromagnetic and modulated phases. As a first step, a discrete set of layerwise mean field equations for the local order parameter mn in the nth layer parallel to the free surface is derived and solved, allowing for a surface field H1 and for interactions JS in the surface plane which differ from the interactions J0 in the bulk, while only in the z-direction perpendicular to the surface competing nearest neighbor ferromagnetic exchange (J1) and next nearest neighbor an…
Statistical Theories of Phase Transitions
2013
The sections in this article are Introduction Phenomenological Concepts Order Parameters and the Landau Symmetry Classification Second-Order Transitions and Concepts about Critical Phenomena (Critical Exponents, Scaling Laws, etc.) Second-Order Versus First-Order Transitions; Tricritical and other Multicritical Phenomena Dynamics of Fluctuations at Phase Transitions Effects of Surfaces and of Quenched Disorder on Phase Transitions: A Brief Overview Computational Methods Dealing with the Statistical Mechanics of Phase Transitions and Phase Diagrams Models for Order–Disorder Phenomena in Alloys Molecular Field Theory and its Generalization (Cluster Variation Method, etc) Computer Simulation T…
Critical behavior of active Brownian particles
2017
We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\…
Phase transitions and phase coexistence: equilibrium systems versus externally driven or active systems - Some perspectives
2021
A tutorial introduction to the statistical mechanics of phase transitions and phase coexistence is presented, starting out from equilibrium systems and nonequilibrium steady-state situations in ext...
Two-dimensional isotropic orientational glasses: a computer-simulation study
1989
The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction. It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to “ferromagnetic” correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT→0, and the critical exponents for this zero-temperature phase transition are estimated. Dynamic correlation functions are analyzed as well and it is s…
Critical Wetting and Interface Localization—Delocalization Transition in a Double Wedge
2004
Using Monte Carlo simulations and finite-size scaling methods we study “wetting” in Ising systems in a L x L x L y pore with quadratic cross section. Antisymmetric surface fields H s act on the free L x L y surfaces of the opposing wedges, and periodic boundary conditions are applied along the y-direction. Our results represent the first simulational observation of fluctuation effects in three dimensional wetting phenomena and corroborate recent predictions on wedge filling. In the limit L → ∞ L y /L 3 = const the system exhibits a new type of phase transition, which is the analog of the “filling transition” that occurs in a single wedge. It is characterized by critical exponents α = 3/4, β…