Estimation of critical behavior from the density of states in classical statistical models

A. Malakis, A. Peratzakis, Nikolaos Fytas

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.
Original languageEnglish
Article number066128
JournalPhysical Review E
Volume70
DOIs
Publication statusPublished - 22 Dec 2004

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Density of States
Critical Behavior
Statistical Model
Specific Heat
Scaling Laws
scaling laws
Critical Exponents
Energy
sampling
specific heat
exponents
Scaling Behavior
Approximation Scheme
statistical mechanics
Statistical Mechanics
Ising
Central limit theorem
Ising model
Ising Model
equivalence

Bibliographical note

The full text is currently unavailable on the repository.

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Estimation of critical behavior from the density of states in classical statistical models. / Malakis, A.; Peratzakis, A.; Fytas, Nikolaos.

In: Physical Review E, Vol. 70, 066128, 22.12.2004.

Research output: Contribution to journalArticle

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