Correlation functions in the two-dimensional random-bond Ising model release_vjvvlfh2e5gvxj6trfq5xc2eue

by S.L.A. de Queiroz, R.B. Stinchcombe

Released as a article .

1996  

Abstract

We consider long strips of finite width L ≤ 13 sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution: P(J_ij)= 1 2 ( δ (J_ij -J_0) + δ (J_ij -rJ_0) ) , 0 < r < 1 . Spin-spin correlation functions <σ_0σ_R> along the "infinite" direction are computed by transfer-matrix methods, at the critical temperature of the corresponding two-dimensional system, and their probability distribution is investigated. We show that, although in-sample fluctuations do not die out as strip length is increased, averaged values converge satisfactorily. These latter are very close to the critical correlation functions of the pure Ising model, in agreement with recent Monte-Carlo simulations. A scaling approach is formulated, which provides the essential aspects of the R-- and L-- dependence of the probability distribution of <σ_0σ_R>, including the result that the appropriate scaling variable is R/L. Predictions from scaling theory are borne out by numerical data, which show the probability distribution of <σ_0σ_R> to be remarkably skewed at short distances, approaching a Gaussian only as R/L ≫ 1 .
In text/plain format

Archived Files and Locations

application/pdf   258.5 kB
file_5envr4kpqbf4fdf6y4oili775q
web.archive.org (webarchive)
archive.org (archive)
core.ac.uk (web)
arxiv.org (repository)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   1996-04-09
Version   v1
Language   en ?
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 65c97d6e-ee03-4cc0-b102-ec208f3da2ea
API URL: JSON