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Title: Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

Abstract

The two-dimensional, q-state (q > 4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Authors:
;
Publication Date:
Research Org.:
Univ. of Minnesota, Minneapolis
OSTI Identifier:
6232362
Resource Type:
Journal Article
Journal Name:
J. Stat. Phys.; (United States)
Additional Journal Information:
Journal Volume: 47:3-4
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CRYSTAL MODELS; MONTE CARLO METHOD; PHASE TRANSFORMATIONS; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; CRYSTAL LATTICES; CURIE-WEISS LAW; FERROMAGNETISM; FLUCTUATIONS; HAMILTONIANS; MAGNETIC SUSCEPTIBILITY; MEAN-FIELD THEORY; ORDER PARAMETERS; PARTICLE INTERACTIONS; QUANTUM FIELD THEORY; RENORMALIZATION; SPIN; STATISTICAL MECHANICS; THERMODYNAMICS; TRANSITION TEMPERATURE; TWO-DIMENSIONAL CALCULATIONS; ANGULAR MOMENTUM; CRYSTAL STRUCTURE; FIELD THEORIES; FUNCTIONS; INTERACTIONS; MAGNETIC PROPERTIES; MAGNETISM; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MECHANICS; PARTICLE PROPERTIES; PHYSICAL PROPERTIES; QUANTUM OPERATORS; SIMULATION; THERMODYNAMIC PROPERTIES; VARIATIONS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; 645400 - High Energy Physics- Field Theory

Citation Formats

Dasgupta, C, and Pandit, R. Testing approximate theories of first-order phase transitions on the two-dimensional Potts model. United States: N. p., 1987. Web. doi:10.1007/BF01007516.
Dasgupta, C, & Pandit, R. Testing approximate theories of first-order phase transitions on the two-dimensional Potts model. United States. https://doi.org/10.1007/BF01007516
Dasgupta, C, and Pandit, R. 1987. "Testing approximate theories of first-order phase transitions on the two-dimensional Potts model". United States. https://doi.org/10.1007/BF01007516.
@article{osti_6232362,
title = {Testing approximate theories of first-order phase transitions on the two-dimensional Potts model},
author = {Dasgupta, C and Pandit, R},
abstractNote = {The two-dimensional, q-state (q > 4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.},
doi = {10.1007/BF01007516},
url = {https://www.osti.gov/biblio/6232362}, journal = {J. Stat. Phys.; (United States)},
number = ,
volume = 47:3-4,
place = {United States},
year = {Fri May 01 00:00:00 EDT 1987},
month = {Fri May 01 00:00:00 EDT 1987}
}