Series and Monte Carlo study of high-dimensional Ising models

• Published in: Journal of statistical physics Vol. 71; no. 5-6; pp. 1221 - 1230
• Main Authors: GOFMAN, M, ADLER, J, AHARONY, A, HARRIS, A. B, STAUFFER, D
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.06.1993
• Subjects: CALCULATION METHODS; COMPUTERIZED SIMULATION; CORRECTIONS; CRITICAL TEMPERATURE; CRYSTAL LATTICES; CRYSTAL MODELS; CRYSTAL STRUCTURE; Exact sciences and technology; ISING MODEL; Lattice theory and statistics (ising, potts, etc.); MAGNETIZATION; MATHEMATICAL MODELS; MECHANICS; MONTE CARLO METHOD; ORDER-DISORDER TRANSFORMATIONS; PHASE TRANSFORMATIONS; PHYSICAL PROPERTIES; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SERIES EXPANSION; SIMULATION; STATISTICAL MECHANICS; Statistical physics, thermodynamics, and nonlinear dynamical systems; THERMODYNAMIC PROPERTIES; TRANSITION TEMPERATURE 662110 > General Theory of Particles & Fields > Theory of Fields & Strings > (1992-); Series expansion; Monte Carlo method; Ising model; Numerical simulation; Critical exponent; High temperature
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/BF01049970

Ising models in high dimensions are used to compare high-temperature series expansions with Monte Carlo simulations. Simulations of the magnetization on four-, six-, and seven-dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data for d = 6 and 7. The authors tabulate 15 terms of series expansions for the susceptibility for general d and give J/k[sub B]T[sub c]= 0.092295 (3) and 0.077706 (2) for d = 6 and 7. In contrast to five dimensions, where earlier series found nonanalytic scaling corrections, for d=6 and 7 the leading scaling correction may be analytic in T- T[sub c]. In most cases these expansions gave more accurate results than these simulations. 16 refs., 7 figs., 1 tab.