Strongly coupled Ising chain under a weak random field

Pier A. Mello and Alberto Robledo

Physica A: Statistical Mechanics and its Applications, 1993, vol. 199, issue 3, 363-386

Abstract: We present here an analytical method based on the transfer matrix M to study quenched disorder in one-dimensional spin systems in the limit of strong couplings and weak disorder. The procedure is formulated for the random-field Ising chain of finite length L, and its properties, represented as functions of M, satisfy a differential equation of the Fokker-Planck type. This equation describes “evolution” with L, and a central-limit theorem of a novel kind provides the equation and its solutions with universal character. We obtain analytical expressions for the moments of the magnetization of the infinite length chain and study the approach to the infinite coupling limit. We find that the random-field free energy fH and the Edwards-Anderson order parameter m2 satisfy a simple relation. We discuss our results in connection to previous work by Luck and Nieuwenhuizen.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:199:y:1993:i:3:p:363-386

DOI: 10.1016/0378-4371(93)90055-9

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