scholarly journals Remarks on the Interpolation Method

2020 ◽  
Vol 181 (4) ◽  
pp. 1218-1238
Author(s):  
Roberto Boccagna ◽  
Davide Gabrielli
Keyword(s):  
Free Energy ◽  
Thermodynamic Limit ◽  
Spin Glasses ◽  
Interpolation Method ◽  
Mean Field ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Mean Field Spin Glasses

Abstract We discuss a generalization of the classic condition of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $$L^2$$ L 2 metric structure of the Gaussian random variables. As an example of application we deduce the existence of the thermodynamic limit for a GREM model with infinite branches for which the classic conditions of validity fail. We underline the dependence of the density of quenched free energy just on the metric structure and discuss the models from a metric viewpoint.

3-D SPIN GLASSES AND ISING MODELS NEW METHODS ON NEW ARCHITECTURES

1993 ◽  
Vol 04 (01) ◽  
pp. 217-221
Author(s):  
GYAN BHANOT
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Ising Model ◽  
Thermodynamic Limit ◽  
Spin Glasses ◽  
Weak Coupling ◽  
Ising Models ◽  
Parallel Architectures ◽  
Strong Indication ◽  
New Methods

I describe work on 3-d Spin Glasses and the 3-d Ising Model done in collaboration with Michael Creutz at BNL and Jan Lacki at IAS Princeton. We have developed novel techniques to study these systems that make use of parallel architectures. For 3-d spin glasses, our results give strong indication that there is no phase transition in the thermodynamic limit whereas for the Ising model, we are able to extend the weak coupling expansion of the average free energy to 50 excited bonds.

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