scholarly journals Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

2003 ◽  
Vol 233 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Francesco Guerra
Keyword(s):  
Spin Glass ◽  
Mean Field ◽  
Spin Glass Model ◽  
Replica Symmetry ◽  
Glass Model ◽  
The Mean

scholarly journals ABOUT THE OVERLAP DISTRIBUTION IN MEAN FIELD SPIN GLASS MODELS

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1675-1684 ◽  
Author(s):  
FRANCESCO GUERRA
Keyword(s):  
Spin Glass ◽  
Order Parameter ◽  
Short Range ◽  
Mean Field ◽  
Spin Glass Model ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Full Agreement ◽  
Rigorous Results ◽  
Glass Model

We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking. As a byproduct, we show that the self-averaging of the Edwards-Anderson fluctuating order parameter, with respect to the external quenched noise, implies that the overlap distribution is given by the Sherrington-Kirkpatrick replica symmetric Ansatz. This extends previous results of Pastur and Scherbina. Finally, we show how to generalize our results to realistic short range spin glass models.

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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