Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution

Abstract

An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q_{ab}^{(\mathrm{RS})}={\delta }_{ab}+q(1-{\delta }_{ab})$ is investigated. In particular, when the expansion is truncated to fourth order in. $Q_{ab}-Q_{ab}^{(\mathrm{RS})}$. The Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns out to exist only in the range of temperature $\mathrm{0.549...}\le T\le T_c=1$, not including T=0. On the other hand an expansion around the paramagnetic solution $Q_{ab}^{(\mathrm{PM})}={\delta }_{ab}$ up to fourth order yields a FRSB solution that exists in a limited temperature range $\mathrm{0.915...}\le T\le T_c=1$.

18 pages, 3 figures

References in corpus (5)

• Low temperature solution of the Sherrington-Kirkpatrick model
• Double Criticality of the Sherrington-Kirkpatrick Model at T=0
• Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature
• New technique for replica symmetry breaking with application to the SK-model at and near T=0
• Full replica symmetry breaking in generalized mean--field spin glasses with reflection symmetry

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• Field theory for zero temperature soft anharmonic spin glasses in a field
• Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick
• Continuous and discontinuous transitions in generalized p-spin glass models
• Generalized Sherrington--Kirkpatrick-glass without reflection symmetry
• Glassy slowdown and replica-symmetry-breaking instantons
• The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution
• Orientational glass: full replica symmetry breaking in generalized spin glass-like models without reflection symmetry
• The Sherrington-Kirkpatrick model near T_c and near T=0
• Full replica symmetry breaking in p-spin-glass-like systems