Legendre Duality of Spherical and Gaussian Spin Glasses

  title={Legendre Duality of Spherical and Gaussian Spin Glasses},
  author={Giuseppe Genovese and Daniele Tantari},
  journal={Mathematical Physics, Analysis and Geometry},
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… 
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