Replica symmetry holds in the SK model for h>0 in the regime β²E[sech⁴(β√q Z + h)] ≤ 1.
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An asymptotic formula for the free energy of the SK model with general sparse variance profile is derived at high temperature, along with an AMP algorithm for its TAP equations.
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Replica symmetry up to the de Almeida-Thouless line in the Sherrington-Kirkpatrick model
Replica symmetry holds in the SK model for h>0 in the regime β²E[sech⁴(β√q Z + h)] ≤ 1.
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The SK model with a sparse variance profile: free energy and AMP algorithm for TAP equations at high temperature
An asymptotic formula for the free energy of the SK model with general sparse variance profile is derived at high temperature, along with an AMP algorithm for its TAP equations.