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Physica A Statistical Mechanics and its Applications

Replica symmetry breaking in the critical behavior in the m-component ferromagnetic spin systems with a short-range disorder

Xintian Wu

Published Mar 1, 1998• 13 citations
Publisher
DOI
10.1016/s0378-4371(97)00464-0

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•Jun 7, 1995•42 citations
The replica symmetry breaking (RSB) is investigated in -component ferromagnetic spin systems with a long-range disorder, with a correlation function obeying a power law . The Landau–Ginzburg Hamiltonian with an RSB quartic interaction term is studied, with the renormalization-group expansion in and , where is the spatial dimension. It is shown that the long-range disorder fixed point found previously is unstable under the perturbation of RSB for and stable for . The RSB fixed points are calculated and there is no physical stable fixed point for .
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- epsilon , 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.
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.