Search results for "statistical physics"

Noise-Induced Phase Transitions

2009

Cluster Algorithms and Reweighting Methods

2019

Roughly at the time (1987) when the manuscript for the first three chapters of the present book was completed, several breakthroughs occurred. They had a profound influence on the scope of Monte Carlo simulations in statistical physics, particularly for the study of phase transitions in lattice models.

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…

Monte Carlo Methods: a powerful tool of statistical physics

1998

Statistical mechanics of condensed matter systems (solids, fluids) tries to express macroscopic equilibrium properties of matter as averages computed from a Hamiltonian that expresses interactions of an atomistic many body system. While analytic methods for most problems involve crude and uncontrolled approximations, the Monte Carlo computer simulation method allows a numerically exact treatment of this problem, apart from “statistical errors” which can be made as small as desired, and the systematic problem that a system of finite size is treated rather than the thermodynamic limit. However, the simulations of phase transitions then elucidate how a symmetry breaking arises via breaking of …

Multicanonical multigrid Monte Carlo method.

1994

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the d-dimensional ${\mathrm{\ensuremath{\Phi}}}^{4}$ field theory in two different situations. First, we study quantum tunneling for d=1 in the continuum limit, and second, we investigate first-order phase transitions for d=2 in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several, and of about one order of magnitude, respectively.

Recent Developments in Monte-Carlo Simulations of First-Order Phase Transitions

1994

In the past few years considerable progress has been made in Monte Carlo simulations of first-order phase transitions and in the analysis of the resulting finite-size data. In this paper special emphasis will be placed on multicanonical simulations using multigrid update techniques, on numerical estimates of interface tensions, and on accurate methods for determining the transition point and latent heat.

Multibondic cluster algorithm for Monte Carlo simulations of first-order phase transitions.

1995

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with $q=7, 10$ and $20$ show that the autocorrelation times of this algorithm grow with the system size $V$ as $\tau \propto V^\alpha$, where the exponent takes the optimal random walk value of $\alpha \approx 1$.

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...

First Versus Second Order Phase Transitions in the Three-Dimensional Three-State Potts Model in Random Fields

1995

The ordering of three-states Potts ferromagnets on the simple cubic lattice exposed to random fields is investigated by extensive Monte Carlo simulations. Evidence is presented that the transition is second order for intermediate strength of the fields, while it presumably is first order for large field strength. The implications for various theoretical predictions are briefly discussed.

Theory of orientational glasses models, concepts, simulations

1992

Abstract This review describes the various attempts to develop a theoretical understanding for ordering and dynamics of randomly diluted molecular crystals, where quadrupole moments freeze in random orientations upon lowering the temperature, as a result of randomness and competing interactions. While some theories attempt to model this freezing into a phase with randomly oriented quadrupole moments in terms of a bond-disorder concept analogous to the Edwards-Anderson model of spin glasses, other theories attribute the freezing to random field-like terms in the Hamiltonian. While models of the latter type have been studied primarily by microscopic molecular field-type treatments, the former…