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Physical review. B, Condensed matter

Explicit renormalization-group analysis of theD=2 random-bond Ising model

Ganpathy N. Murthy

Published Jul 1, 1987• 6 citations
Publisher

Abstract

It is shown by an explicit momentum-space renormalization-group analysis that the true renormalization-group equations for the D=2 random-bond Ising model agree with the equations obtained using the replica trick.
DOI
10.1103/physrevb.36.766

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Real space renormalisation group techniques and the replica method of Edwards and Anderson (1975), combined with successive variational approximations going beyond mean field, are used to calculate phase diagrams of various Ising systems. For a bond dilute 2D Ising model with nearest-neighbour interactions, real-space renormalisation group techniques provide very precise results which are used to test the reliability of the replica method. Combined with variational approximations going beyond mean field, this last method is applied to 3D Ising models with competing nearest-neighbour and next-nearest-neighbour interactions.
We introduce a procedure which considerably simplifies the calculation of clusters like those commonly appearing in real-space renormalization-group treatments of bond-percolation and pure and random Ising and Potts problems. The method is illustrated through two applications for the qqq-state Potts ferromagnet.