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Physical Review Letters

High-Temperature Series Analysis of 2D Random-Bond Ising Ferromagnets

Alexandra Roder, Joan Adler, Wolfhard Janke E

Published May 25, 1998• 40 citations
Publisher

Abstract

We analyze new high-temperature series expansions for the susceptibility $\ensuremath{\chi}$ of the two-dimensional random-bond Ising ferromagnet with a symmetric bimodal distribution of two positive couplings ${J}_{1}$ and ${J}_{2}$. By studying a wide range of coupling ratios ${J}_{2}/{J}_{1}$ we obtain compelling evidence for a critical behavior of the form $\ensuremath{\chi}\ensuremath{\sim}{t}^{\ensuremath{-}7/4}|\mathrm{ln}t{|}^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig.

DOI
10.1103/physrevlett.80.4697

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We analyze new high-temperature series expansions for the susceptibility \ensuremathχ\ensuremath{\chi}\ensuremathχ of the two-dimensional random-bond Ising ferromagnet with a symmetric bimodal distribution of two positive couplings J1{J}_{1}J1​ and J2{J}_{2}J2​. By studying a wide range of coupling ratios J2/J1{J}_{2}/{J}_{1}J2​/J1​ we obtain compelling evidence for a critical behavior of the form \ensuremathχ\ensuremath∼t\ensuremath−7/4∣lnt∣7/8\ensuremath{\chi}\ensuremath{\sim}{t}^{\ensuremath{-}7/4}|\mathrm{ln}t{|}^{7/8}\ensuremathχ\ensuremath∼t\ensuremath−7/4∣lnt∣7/8, as predicted theoretically by Shalaev, Shankar, and Ludwig.
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