Degeneracy Algorithm for Random Magnets

Abstract

It has been known for a long time that the ground state problem of random magnets, e.g. random field Ising model (RFIM), can be mapped onto the max-flow/min-cut problem of transportation networks. I build on this approach, relying on the concept of residual graph, and design an algorithm that I prove to be exact for finding all the minimum cuts, i.e. the ground state degeneracy of these systems. I demonstrate that this algorithm is also relevant for the study of the ground state properties of the dilute Ising antiferromagnet in a constant field (DAFF) and interfaces in random bond magnets.Comment: 17 pages(Revtex), 8 Postscript figures(5color) to appear in Phys. Rev. E 58, December 1st (1998