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

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  • Wu, Xin-tian

Abstract

We investigate the replica symmetry breaking (RSB) in m-component ferromagnetic spin systems with a short-range disorder. Using ε-expansion the Landau–Ginzburg Hamiltonian with a RSB quartic interaction term is studied, where ε=4−d, d is the spatial dimension. The differential recursion relations of renormalization group (RG) are derived to the second order of ε. The replicon eigenvalue, which is a simple way to investigate the stability with respect to the continuous RSB modes, is defined. The fixed points and their eigenvalues are obtained. For mmc, we find a stable fixed point, which is not only stable in the one-step RSB subspace but also stable with respect to the continuous RSB. However, it is unphysical. For m>mc only the pure fixed point is physical and stable.

Suggested Citation

  • Wu, Xin-tian, 1998. "Replica symmetry breaking in the critical behavior in the m-component ferromagnetic spin systems with a short-range disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(3), pages 309-319.
    • Handle: RePEc:eee:phsmap:v:251:y:1998:i:3:p:309-319
    DOI: 10.1016/S0378-4371(97)00464-0
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