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Statements

Subject Item
dbr:Cavity_method
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Cavity method
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The cavity method is a mathematical method presented by Marc Mézard, Giorgio Parisi and Miguel Angel Virasoro in 1987 to solve some mean field type models in statistical physics, specially adapted to disordered systems. The method has been used to compute properties of ground states in many condensed matter and optimization problems. The cavity method has proved useful in the solution of optimization problems such as k-satisfiability and graph coloring. It has yielded not only ground states energy predictions in the average case, but also has inspired algorithmic methods.
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1099402128
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dbr:Giorgio_Parisi dbr:Miguel_Ángel_Virasoro_(physicist) dbr:Marc_Mézard dbr:Mean_field dbr:Boolean_satisfiability_problem dbr:Spin_glass dbr:Sherrington–Kirkpatrick_model dbr:Replica_trick dbr:Graph_coloring dbr:Optimization_problem dbr:Statistical_physics dbr:Belief_propagation dbr:Condensed_matter dbr:Hans_Bethe dbr:Ground_state dbc:Condensed_matter_physics dbr:Rudolf_Peierls
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The cavity method is a mathematical method presented by Marc Mézard, Giorgio Parisi and Miguel Angel Virasoro in 1987 to solve some mean field type models in statistical physics, specially adapted to disordered systems. The method has been used 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, the cavity method has shown wider applicability. It can be regarded as a generalization of the Bethe—Peierls iterative method in tree-like graphs, to the case of a graph with loops that are not too short. The different approximations that can be done with the cavity 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. The cavity method has proved useful in the solution of optimization problems such as k-satisfiability and graph coloring. It has yielded not only ground states energy predictions in the average case, but also has inspired algorithmic methods.
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