Replica symmetric spin glass field theory
arXiv:cond-mat/0612523 · doi:10.1016/j.nuclphysb.2007.03.006
Abstract
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d<6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
38 pages, 1 figure
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Cited by in corpus (9)
- Behavior of Ising Spin Glasses in a Magnetic Field
- Replica symmetry breaking in and around six dimensions
- Almeida-Thouless transition below six dimensions
- Evidence against an Almeida-Thouless line in disordered systems of Ising dipoles
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- Interaction-Flip Identities in Spin Glasses
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- Orientational glass: full replica symmetry breaking in generalized spin glass-like models without reflection symmetry
- Logarithmic critical slowing down in complex systems: from statics to dynamics