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 paper recounts Talagrand's 2006 proof of the Parisi formula for the Sherrington-Kirkpatrick model and related structural results that made mean-field spin glass theory rigorous.
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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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Michel Talagrand and the Rigorous Theory of Mean Field Spin Glasses
The paper recounts Talagrand's 2006 proof of the Parisi formula for the Sherrington-Kirkpatrick model and related structural results that made mean-field spin glass theory rigorous.