Replica symmetric spin glass field theory

Details Replica symmetric spin glass field theory Replica symmetric spin glass field theory

2006-12-20

arxiv.org/abs/cond-mat/0612523v1

Nuclear Physics B, Volume 772, Issue 3, 18 June 2007, Pages 340-370

Physics

Condensed Matter

Disordered Systems and Neural Networks

38 pages, 1 figure

Scientific paper

10.1016/j.nuclphysb.2007.03.006

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.

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