Monte Carlo tests of theoretical predictions for critical phenomena: still a problem?

• Published in: Computer physics communications Vol. 127; no. 1; pp. 126 - 130
• Main Authors: Binder, K., Luijten, E.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01-05-2000; Elsevier Science
• Subjects: Classical spin models; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Condensed matter: structure, mechanical and thermal properties; Critical behavior; Critical point phenomena; Crossover phenomena; Equations of state, phase equilibria, and phase transitions; Equilibrium properties near critical points, critical exponents; Exact sciences and technology; Finite-size scaling; General studies of phase transitions; General theory and models of magnetic ordering; Long-range interactions; Magnetic properties and materials; Monte Carlo; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Thermodynamics; 75.10.Hk; 64.60.Fr; Crossover phenomena; 05.70.Jk; Monte Carlo; Critical behavior; Long-range interactions; Finite-size scaling; Finite size effect; Scaling function; Monte Carlo methods; Long range interaction; Theoretical study; Ferromagnetic materials; Ising model; Crossover study
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(00)00015-1

Two Monte Carlo studies of critical behavior in ferromagnetic Ising models are described: the first one deals with the crossover from the Ising class to the mean field class, when the interaction range increases. The second study deals with the finite size behavior at dimensionalities above the marginal dimension where Landau theory applies. The numerical results are compared to pertinent theoretical predictions, and unsolved problems are briefly described.