Combinatorial Optimization and the Physics of Disordered Systems

Abstract

The purpose of this chapter of this monograph is to confront the reader with a number of optimization algorithms that are exact and polynomial in time and which have interesting applications in the physics of disordered systems. These are solid materials which contain a substantial degree of quenched disorder, have been an experimental and a theoretical challenge for physicists for many decades. The different thermodynamic phases emerging in random magnets, the aging properties and memory effects of spin glasses, the disorder induced conductor-to-insulator transition in electronic or bosonic systems, the collective behaviour of magnetic flux lines in amorphous high temperature superconductors, and the roughening transition of a disordered charge density wave systems are only a few examples for these fascinating phenomena that occur due to the presence of quenched disorder.