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On the replica symmetric solution for the Sherrington-Kirkpatrick model. (English) Zbl 0899.60096

Summary: We prove that replica symmetric equations for the free energy and Edvards-Anderson order parameter for the Sherrington-Kirkpatrick model with Gaussian magnetic field hold above some line on the \(T\)-\(h\) plane. This line coincides with AT-line at the point \(h=0\) and behaves similarly as \(T\to 0\).

MSC:

60K40 Other physical applications of random processes
82B27 Critical phenomena in equilibrium statistical mechanics
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