Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2005-04-18
Phys. Rev. E, 72, 026125 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
21 pages RevTex, 8 figures
Scientific paper
10.1103/PhysRevE.72.026125
We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several different domains and various problems in one dimension such as the so called descent problem. We first motivate our method by analyzing these problems using the annealed approximation, then the limit of a large number of points we develop a formalism to carry out the quenched calculation. This formalism does not require the replica method and its predictions are found to agree with Monte Carlo simulations. In addition our method reproduces an exact mathematical result for the Maximum traveling salesman problem in two dimensions and suggests its generalization to higher dimensions. The general approach may provide an alternative method to study certain systems with quenched disorder.
Dean David S.
Lancaster David
Majumdar Satya N.
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