Finite size corrections to disordered systems on Erdös-Rényi random graphs

Abstract

We study the finite size corrections to the free energy density in disorder spin systems on sparse random graphs, using both replica theory and cavity method. We derive an analytical expressions for the $O(1/N)$ corrections in the replica symmetric phase as a linear combination of the free energies of open and closed chains. We perform a numerical check of the formulae on the Random Field Ising Model at zero temperature, by computing finite size corrections to the ground state energy density.

Submitted to PRB

References in corpus (3)

• The high temperature region of the Viana-Bray diluted spin glass model
• On Cavity Approximations for Graphical Models
• Stability of the replica-symmetric saddle-point in general mean-field spin-glass models

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