Accurate Monte Carlo critical exponents for Ising lattices

2003/04/02 by J. G. Garcia, Jorge Garcı́a, Julio A. Gonzalo +1
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1016/s0378-4371(03)00362-5

5 pages, 4 figures. Sent to Europhysics Letters

arxiv created 2003/04/02 · openalex publication_date 2003/06/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Monte Carlo investigations of magnetization versus field, M_c(H), at the critical temperature provide direct accurate results on the critical exponent δ^-1 for one, two, three and four-dimensional lattices: δ_1D^-1=0, δ_2D^-1=0.0666(2)≃1/15, δ_3D^-1=0.1997(4)≃1/5, δ_4D^-1=0.332(5)≃1/3. This type of Monte Carlo data on δ, which is not easily found in studies of Ising lattices in the current literature, as far as we know, defines extremely well the numerical value of this exponent within very stringent limits.

Citations

• Equation of State Calculations by Fast Computing Machines
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Critical temperatures of the d=3, s=1/2Ising model; the effect of confluent corrections to scaling
• Statistical Mechanics of Phase Transitions