scholarly journals Thouless–Anderson–Palmer Equations for the Ghatak–Sherrington Mean Field Spin Glass Model

2021 ◽  
Vol 184 (2) ◽  
Author(s):  
Antonio Auffinger ◽  
Cathy Xi Chen
Keyword(s):  
Spin Glass ◽  
Mean Field ◽  
Spin Glass Model ◽  
Glass Model

scholarly journals An investigation of the hidden structure of states in a mean-field spin-glass model

1997 ◽  
Vol 30 (20) ◽  
pp. 7021-7038 ◽  
Author(s):  
Andrea Cavagna ◽  
Irene Giardina ◽  
Giorgio Parisi
Keyword(s):  
Spin Glass ◽  
Mean Field ◽  
Spin Glass Model ◽  
Glass Model

scholarly journals Rigorous solution of a mean field spin glass model

2000 ◽  
Vol 13 (2) ◽  
pp. 147-160
Author(s):  
T. C. Dorlas ◽  
J. R. Wedagedera
Keyword(s):  
Spin Glass ◽  
Large Deviation ◽  
Mean Field ◽  
Almost Sure Convergence ◽  
Thermodynamic Quantities ◽  
Convergence Criteria ◽  
Spin Glass Model ◽  
Rigorous Solution ◽  
Glass Model ◽  
Null Set

A separable spin glass model whose exchange integral takes the form Jij=J(ξi1ξj2+ξi2ξj1) which was solved by van Hemmen et al. [12] using large deviation theory [14] is rigorously treated. The almost sure convergence criteria associated with the cumulant generating function C(t) with respect to the quenched random variables ξ is carefully investigated, and it is proved that the related excluded null set 𝒩 is independent of t. The free energy and hence the other thermodynamic quantities are rederived using Varadhan's Large Deviation Theorem. A simulation is also presented for the entropy when ξ assumes a Gaussian distribution.

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