scholarly journals Replica derivation of Sompolinsky free energy functional for mean field spin glasses

1981 ◽  
Vol 42 (23) ◽  
pp. 523-526 ◽  
Author(s):  
C. de Dominicis ◽  
M. Gabay ◽  
H. Orland
Keyword(s):  
Free Energy ◽  
Spin Glasses ◽  
Mean Field ◽  
Energy Functional ◽  
Free Energy Functional ◽  
Mean Field Spin Glasses

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.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Droplet minimizers for the Gates–Lebowitz–Penrose free energy functional

Nonlinearity ◽  
2009 ◽  
Vol 22 (12) ◽  
pp. 2919-2952 ◽  
Author(s):  
E A Carlen ◽  
M C Carvalho ◽  
R Esposito ◽  
J L Lebowitz ◽  
R Marra
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Free Energy Functional
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