Optimization problems and replica symmetry breaking in finite connectivity spin glasses
Abstract
A formalism capable of handling the first step of hierarchical replica symmetry breaking (RSB) in finiteconnectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field distributions (or, equivalently magnetization distributions) inside the cluster of states. The approach is shown to coincide with previous works in the replicasymmetric case and in the two limiting cases m = 0 and 1 where m is Parisi's break point. As an application to the study of optimization problems, the GS properties of the random 3satisfiability problem are investigated and we present a first RSB solution improving replicasymmetric results.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 1998
 DOI:
 10.1088/03054470/31/2/012
 arXiv:
 arXiv:condmat/9707089
 Bibcode:
 1998JPhA...31..513M
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 16 pages Revtex file, 1 figure