Potts models: Density of states and mass gap from Monte Carlo calculations

Nelson A. Alves, Bernd A. Berg, and Ramon Villanova
Phys. Rev. B 43, 5846 – Published 1 March 1991
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Abstract

Monte Carlo simulations are performed for first-order phase-transition models. The three-dimensional three-state Potts model has a weak first-order transition. For this model we calculate the density of states on L3 block lattices (L up to size 36) and obtain high-precision estimates for the leading partition-function zeros. The finite-size-scaling analysis of the first zero exhibits the expected convergence of the critical exponent ν toward 1/D for large L; in particular, we find ν=2.955(26) from our two largest lattices. Analysis of our specific-heat Cv data yields l=0.080 31(26) for the latent heat. Along another line of approach, we calculate the mass gap m=1/ξ (ξ is the correlation length) for cylindrical L2Lz lattices (L up to 24 and Lz=256). The finite size-scaling analysis of these results is also consistent with the convergence of ν toward 1/D, but that the limiting value is 1/D is not yet conclusively established. Some theoretical arguments favor ν→0 in case of a first-order transition in a cylindrical LD1∞ geometry. Therefore, we also applied our approach to the 2D ten-state Potts model, which is known to have a strong first-order transition. In this case we find unambiguous evidence in favor of 1/D as the limiting value.

  • Received 9 October 1990

DOI:https://doi.org/10.1103/PhysRevB.43.5846

©1991 American Physical Society

Authors & Affiliations

Nelson A. Alves, Bernd A. Berg, and Ramon Villanova

  • Supercomputer Computations Research Institute and Department of Physics, The Florida State University, Tallahassee, Florida 32306

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Issue

Vol. 43, Iss. 7 — 1 March 1991

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