Two-sided bounds on the free energy from local states in Monte Carlo simulations

Journal Article · Tue Aug 01 00:00:00 EDT 1989 · Journal of Statistical Physics; (USA)

DOI:https://doi.org/10.1007/BF01044436· OSTI ID:6140149

Schlijper, A G ^[1]; Smit, B ^[2]

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1. Koninklijke/Shell Exploratie en Produktie Laboratorium, Rijswijk (Netherlands)
2. Koninklijke/Shell Laboratorium Amsterdam (Netherlands)

The authors show that a precise assessment of free energy estimates in Monte Carlo simulations of lattice models is possible by using cluster variation approximations in conjunction with the local states approximations proposed by Meirovitch. The local states method (LSM) utilizes entropy expressions which recently have been shown to correspond to a converging sequence of upper bounds on the thermodynamic limit entropy density (i.e., entropy per lattice site), whereas the cluster variation method (CVM) supplies formulas that in some cases have been proven to be, and in other cases are believed to be, lower bounds. They have investigated CVM-LSM combinations numerically in Monte Carlo simulations of the two-dimensional Ising model and the two-dimensional five-states ferromagnetic Potts model. Even in the critical region the combination of upper and lower bounds enables an accurate and reliable estimation of the free energy from data of a single run. CVM entropy approximations are therefore useful in Monte Carlo simulation studies and in establishing the reliability of results from local states methods.

• OSTI ID: 6140149
• Journal Information: Journal of Statistical Physics; (USA), Journal Name: Journal of Statistical Physics; (USA) Vol. 56:3-4; ISSN 0022-4715; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
ENERGY
ENERGY LEVELS
ENTROPY
FERROMAGNETIC MATERIALS
FREE ENERGY
ISING MODEL
MAGNETIC MATERIALS
MATERIALS
MATHEMATICAL MODELS
MECHANICS
MONTE CARLO METHOD
PHYSICAL PROPERTIES
RELIABILITY
STATISTICAL MECHANICS
THERMODYNAMIC PROPERTIES
THERMODYNAMICS
TWO-DIMENSIONAL CALCULATIONS