Renormalization-Group Approach to the Critical Behavior of Random-Spin Models

1974/12/23 by A. B. Harris, T. C. Lubensky · 6 citations
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Complex Network Analysis Techniques

paper · doi:10.1103/physrevlett.33.1540

openalex publication_date 1974/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/21

Abstract

A renormalization-group technique is used to study the critical behavior of spin models in which each interaction has a small independent random width about its average value. The cluster approximation of Niemeyer and Van Leeuwen indicates that the two-dimensional Ising model has the same critical behavior as the homogeneous system. The \ensuremathε expansion for n-component continuous spins shows that this behavior holds to first order in \ensuremathε for n>4. For n<4, there is a new stable fixed point with 2\ensuremathν=1+[\frac3n16(n\ensuremath-1)]\ensuremathε.

Citations

• Effect of random defects on the critical behaviour of Ising models

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• A. Brooks Harris [wikipedia]