Legendre Duality of Spherical and Gaussian Spin Glasses

  • Giuseppe GenoveseEmail author
  • Daniele Tantari


The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.


Spin glasses Spherical model Neural networks 

Mathematics Subject Classification (2010)

60F10 60K35 82B44 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Centro Ennio de GiorgiScuola Normale Superiore di PisaPisaItaly

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