The phase diagram of Lévy spin glasses

Abstract

We study a fully connected spin-glass model in which the coupling strengths are drawnfrom a Lévy distribution. In this model each spin can be seen as interacting through afinite number of strong bonds and an infinite number of weak bonds, due to thelarge tail behavior of the coupling distribution. We solve the model through thereplica and the cavity method. The hybrid behavior of Lévy spin glasses becomestransparent in our solution: the local field contains a part propagating along abackbone of strong bonds and a Gaussian noise term due to weak bonds. Our methodallows us to determine the complete replica symmetric phase diagram, the replicasymmetry breaking line and the entropy. The results are compared with ones fromsimulations and previous calculations using a Gaussian ansatz for the distribution offields.