The Cavity method is a mathematical method due to M. Mezard, G. Parisi and M.A. Virasoro in 1985 to compute properties of ground states in many condensed matter and optimization problems. Initially invented to deal with the Sherrington Kirkpatrick model of spin glasses, it has shown wide applicability. It can be regarded as a generalization of he BethePeierls iterative method in tree-like graphs to the case of graph with loops that are not too short. The different approximations that can be done with the replica method are usually named after their equivalent with the different steps of the replica method which is mathematically more subtle and less intuitive than the cavity approach. Parisi is a municipality/county in the state of São Paulo in Brazil. ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ... It has been suggested that Solid state physics be merged into this article or section. ... In computer science, an optimization problem is the problem to find among all feasible solutions for some problem the best one. ... Hans Bethe Hans Albrecht Bethe (pronounced Bay-tuh; July 2, 1906 – March 6, 2005), was a German-American physicist who won the Nobel Prize in Physics for 1967 for his discovery of stellar nucleosynthesis. ...
The cavity method has played and is paying a major role in the solution of optimization problems like the K-satisfiability and the graph coloring in present days. It has yielded not only ground states energy predictions in the average case, but also has inspired algorithmic methods for solving particular instances of an optimization problem. In computer science, an optimization problem is the problem to find among all feasible solutions for some problem the best one. ... A 3-coloring suits this graph, but fewer colors would result in adjacent vertices of the same color. ... In computer science, an optimization problem is the problem to find among all feasible solutions for some problem the best one. ...
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