scholarly journals Mean-field theory for a spin-glass model of neural networks: TAP free energy and the paramagnetic to spin-glass transition

1997 ◽  
Vol 30 (23) ◽  
pp. 8085-8094 ◽  
Author(s):  
K Nakanishi ◽  
H Takayama
Keyword(s):  
Field Theory ◽  
Neural Networks ◽  
Free Energy ◽  
Glass Transition ◽  
Spin Glass ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Glass Model ◽  
Spin Glass Transition ◽  
Glass Model

Temperature Dependence of Spatial and Dynamic Heterogeneities above the Ising Spin Glass Transition

1996 ◽  
Vol 455 ◽  
Author(s):  
S. C. Glotzer ◽  
P. H. Poole ◽  
A. Coniglio ◽  
N. Jan
Keyword(s):  
Glass Transition ◽  
Temperature Dependence ◽  
Spin Glass ◽  
Large Scale ◽  
Spin Glass Model ◽  
Ising Spin Glass ◽  
Ising Spin ◽  
Spin Glass Transition ◽  
Glass Model ◽  
Equilibrium Distributions

ABSTRACTThe temperature dependence of the microstructure and local dynamics in the paramagnetic phase of the d = 2 and d = 3 ± J Ising spin glass model is examined by comparing the equilibrium distributions of local flip-rates and local energies calculated in large-scale Monte Carlo simulations. The emergence in this model of fast processes as the glass transition is approached corresponds with recent experimental results.

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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