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

Ulisse Ferrari, Carlo Lucibello, Flaviano Morone, Giorgio Parisi, Federico Ricci-Tersenghi, Tommaso Rizzo

Published 2013-05-14, updated 2013-10-01Version 3

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.