Large Energy Cumulants in the 2D Potts Model and their Effects in Finite Size Analysis

Abstract

We develop an ansatz for expressing the free energy of the two dimensional $q$-states Potts model for $q>4$ near its first order phase transition point. We notice that for the moderate values of $q\lesssim 15$, the energy profile at the phase transition is not expressible as a sum of gaussians. We discuss how this affects the traditional finite size analysis of this phase transition. In particular, the dominant length scale governing the finite size corrections turns out to be much ($\sim 6$ ~times) larger than the largest correlation length in the problem.

20 pages Plain TeX,16 Postscipt figures available by ftp anonymous on amoco.saclay.cea.fr as ftp://amoco.saclay.cea.fr/pubs.spht/94-008.fig.ps SPht-94/008

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Cited by in corpus (9)

• 2D Potts Model Correlation Lengths: Numerical Evidence for ${\xi }_o={\xi }_d$ at ${\beta }_t$
• FINITE SIZE SCALING FOR FIRST ORDER TRANSITIONS: POTTS MODEL
• Large-$q$ expansion of the specific heat for the two-dimensional $q$-state Potts model
• Fisher Zeroes and Singular Behaviour of the Two Dimensional Potts Model in the Thermodynamic Limit
• Large-q expansion of the energy and magnetization cumulants for the two-dimensional q-state Potts model
• Correlation Length From Cluster-Diameter Distribution
• Singular Behaviour of the Potts Model in the Thermodynamic Limit
• Phenomenological theory of the Potts model evaporation-condensation transition
• Large-$q$ expansion of the two-dimensional $q$-state Potts model by the finite lattice method