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 finite-connectivity 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 replica-symmetric 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 3-satisfiability problem are investigated and we present a first RSB solution improving replica-symmetric results.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- January 1998
- DOI:
- 10.1088/0305-4470/31/2/012
- arXiv:
- arXiv:cond-mat/9707089
- Bibcode:
- 1998JPhA...31..513M
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 16 pages Revtex file, 1 figure