Observation of fss for a first order phase transition

Alain H. Billoire, T. Neuhaus, Universität Bielefeld, Bernd A. Berg

Published Jan 1, 1993• 33 citations

Abstract

We present the results of a multicanonical simulation of the q=20 2-d Potts model in the transition region. This is a very strong first order phase transition. We observe, for the first time, the asymptotic finite size scaling behavior predicted by Borgs and Koteck´y close to a first order phase transition point. SPhT-92/120

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Observation of fss for a first order phase transition

Alain H. Billoire, T. Neuhaus, Universität Bielefeld, Bernd A. Berg

Published Jan 1, 1993• 33 citations

OpenAlex

Abstract

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{\mathit{U}}_{0}

(

{\mathit{tL}}^{\mathit{d}}

)+${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{d}}$

{\mathit{U}}_{1}

(

{\mathit{tL}}^{\mathit{d}}

) with t=1-

{\mathit{T}}_{\mathit{c}}

/T. In particular, we consider the specific heat and Binder's fourth cumulant and show this has a minimum value of 2/3-(

{\mathit{e}}_{1}

{\mathit{e}}_{2}

{\mathit{e}}_{2}

{\mathit{e}}_{1}

{)}^{2}

/12+O(${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{d}}$) at a temperature

{\mathit{T}}_{\mathit{c}}^{(2)}

(L)-

{\mathit{T}}_{\mathit{c}}

=O(${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{d}}$). Various other pseudocritical temperatures corresponding to extrema of other cumulants are evaluated. We compare these theoretical predictions with extensive Monte Carlo simulations of the nominally strong first-order transitions in the eight- and ten-state Potts models in two dimensions for system sizes L\ensuremath{\le}50. The ten-state simulations agree with theory in all details in contrast to the eight-state data, and we give estimates for the bulk specific heats at

{\mathit{T}}_{\mathit{c}}

using all exactly known analytic results. A criterion is developed to estimate numerically whether or not system sizes used in a simulation of a first-order transition are in the finite-size-scaling regime.