Scaling and finite-size scaling in the two-dimensional randomly coupled Ising ferromagnet

1999/05/14 by Jae-Kwon Kim · 1 citation
Mathematics · Physics and Astronomy · #Condensed matter physics #Ferromagnetism #Geometry #Ising model #Markov Chains and Monte Carlo Methods #Mathematics #Physics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.61.1246

9 pages, 4figuers

arxiv created 1999/05/14 · openalex publication_date 2000/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

It is shown by the Monte Carlo method that finite-size scaling (FSS) holds in the two-dimensional randomly coupled Ising ferromagnet. It is also demonstrated that the form of the universal FSS function constructed via a FSS scheme depends on the strength of the random coupling in the case of strongly disordered systems. Monte Carlo measurements of thermodynamic (infinite-volume-limit) data of the correlation length (\ensuremathξ) up to \ensuremathξ\ensuremath≃200 along with measurements of the fourth-order cumulant ratio (Binder cumulant ratio) at criticality are analyzed in light of two competing scenarios of weak universality and the multiplicative logarithmic correction. It is demonstrated that the data are likely to be more consistent with the former scenario than the latter which is the conventional scenario.

Citations

• Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach
• Fermionic structure of two-dimensional Ising model with quenched site dilution
• The critical behaviour of the two-dimensional dilute Ising magnet
• Critical behaviour of the phase transition in the 2D Ising Model with impurities

Cited by

• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet