Department of Physics Papers

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Journal Article

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Journal of Physics A: Mathematical and General



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We study the critical properties of the weakly disordered p-component random Heisenberg ferromagnet. It is shown that if the specific-heat critical exponent of the pure system is positive, the traditional renormalization group (RG) flows at dimensions D=4-ε, which are usually considered as describing the disorder-induced universal critical behaviour, are unstable with respect to replica-symmetry breaking (RSB) potentials such as those found in spin glasses. It is demonstrated that the RG flows involving RSB potentials lead to fixed points which have a structure known as the one-step RSB, and there exists a whole spectrum of such fixed points. It is argued that spontaneous RSB can occur due to the interactions of the fluctuating fields with the local non-perturbative degrees of freedom coming from the multiple local minima solutions of the mean-field equations. However, it is not clear whether or not RSB occurs for infinitesimally weak disorder. Physical consequences of these conclusions are discussed.

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This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and General. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at

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Date Posted: 20 August 2015

This document has been peer reviewed.