arXiv:hep-lat/9404002 · Europhysics Letters (EPL)

Critical-Point Correlation Function for the 2D Random Bond Ising Model

A. L Talapov, Щур Лев Николаевич

Published Jul 20, 1994• 30 citations

Abstract

High-accuracy Monte Carlo simulation results for a 1024 * 1024 Ising system with ferromagnetic impurity bonds are presented. The spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since the critical temperature for the system with impurities is almost two times lower than pure Ising T c . Finite corrections to the correlation function due to combined action of impurities and finite lattice size are described.

DOI: 10.1209/0295-5075/27/3/004

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arXiv:hep-lat/9404002 · Europhysics Letters (EPL)

Critical-Point Correlation Function for the 2D Random Bond Ising Model

A. L Talapov, Щур Лев Николаевич

Published Jul 20, 1994• 30 citations

arXiv HTML PDF

Abstract

DOI: 10.1209/0295-5075/27/3/004

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Виктор Степанович Доценко, Vl.S. Dotsenko

Journal of Physics C Solid State PhysicsJun 20, 198220 citations

T_c

. Small deviations from the pure behaviour contradict to some of the competing theories.

We consider long strips of finite width L\ensuremath{\le}13 sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution P(

{\mathit{J}}_{\mathit{ij}}

)=1/2[\ensuremath{\delta}(

{\mathit{J}}_{\mathit{ij}}

{\mathit{J}}_{0}

)+\ensuremath{\delta}(

{\mathit{J}}_{\mathit{ij}}

{\mathit{rJ}}_{0}

)], 0r1. Spin-spin correlation functions 〈${\mathrm{\ensuremath{\sigma}}}_{0}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}$〉 along the ``infinite'' direction are computed by transfer-matrix methods, at the critical temperature of the corresponding two-dimensional system, and their probability distribution is investigated. We show that, although in-sample fluctuations do not die out as strip length is increased, averaged values converge satisfactorily. These latter are very close to the critical correlation functions of the pure Ising model, in agreement with recent Monte Carlo simulations. A scaling approach is formulated, which provides the essential aspects of the R and L dependence of the probability distribution of ln〈${\mathrm{\ensuremath{\sigma}}}_{0}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}$〉, including the result that the appropriate scaling variable is R/L. Predictions from scaling theory are borne out by numerical data, which show the probability distribution of ln〈${\mathrm{\ensuremath{\sigma}}}_{0}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}$〉 to be remarkably skewed at short distances, approaching a Gaussian only as R/L\ensuremath{\gg}1. \textcopyright{} 1996 The American Physical Society.