Replica symmetry breaking in and around six dimensions

Details Replica symmetry breaking in and around six dimensions Replica symmetry breaking in and around six dimensions

2011-11-14

arxiv.org/abs/1111.3313v1

Nucl. Phys. B 858, 293-316 (2012)

Physics

Condensed Matter

Disordered Systems and Neural Networks

28 pages,4 figures

Scientific paper

10.1016/j.nuclphysb.2012.01.014

Two, replica symmetry breaking specific, quantities of the Ising spin glass --- the breakpoint x1 of the order parameter function and the Almeida-Thouless line --- are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results comfirm that replica symmetry breaking does exist below d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x1 has a nonzero and universal value for d<6 at criticality. Near six dimensions we have x1=3(6-d)+O[(6-d)^2]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.

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