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

• Published in: Physical review. B, Condensed matter Vol. 43; no. 7; pp. 5846 - 5856
• Main Authors: ALVES, N. A, BERG, B. A, VILLANOVA, R
• Format: Journal Article
• Language: English
• Published: Woodbury, NY American Physical Society 01-03-1991; American Institute of Physics
• Subjects: 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-); CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Condensed matter: structure, mechanical and thermal properties; CRYSTAL MODELS; ENERGY-LEVEL DENSITY; Equations of state, phase equilibria, and phase transitions; Exact sciences and technology; FUNCTIONS; General studies of phase transitions; ISING MODEL; MATHEMATICAL MODELS; MONTE CARLO METHOD; PARTITION FUNCTIONS; PHASE TRANSFORMATIONS; PHYSICAL PROPERTIES; Physics; SPECIFIC HEAT; THERMODYNAMIC PROPERTIES; Specific heat; Finite size effect; Monte Carlo method; Phase transformation; Density of states; Three dimensional model; Partition function; Theoretical study; Critical phenomenon; Potts model; Correlation length
• ISSN: 0163-1829; 1095-3795
• DOI: 10.1103/PhysRevB.43.5846

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 {ital L}{sup 3} block lattices ({ital 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 {nu} toward 1/{ital D} for large {ital L}; in particular, we find {nu}=2.955(26) from our two largest lattices. Analysis of our specific-heat {ital C}{sub {ital v}} data yields {ital l}=0.080 31(26) for the latent heat. Along another line of approach, we calculate the mass gap {ital m}=1/{xi} ({xi} is the correlation length) for cylindrical {ital L}{sup 2}{ital L}{sub {ital z}} lattices ({ital L} up to 24 and {ital L}{sub {ital z}}=256). The finite size-scaling analysis of these results is also consistent with the convergence of {nu} toward 1/{ital D}, but that the limiting value is 1/{ital D} is not yet conclusively established. Some theoretical arguments favor {nu}{r arrow}0 in case of a first-order transition in a cylindrical {ital L}{sup {ital D}{minus}1}{infinity} 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/{ital D} as the limiting value.