Numerical estimate of finite size corrections to the free energy of the SK model using Guerra--Toninelli interpolation

TL;DR

This paper numerically investigates finite size corrections to the free energy of the SK model using Guerra--Toninelli interpolation, confirming theoretical predictions about their asymptotic behavior at and below the critical temperature.

Contribution

It provides the first numerical verification of the predicted finite size correction behaviors in the SK model using an interpolating formula.

Findings

Finite size corrections at T_c follow a (1/12 N) log(N/N_0) pattern.

Below T_c, corrections behave as 1/N^{2/3}.

Results align with theoretical predictions by Parisi, Ritort, and Slanina.

Abstract

I use an interpolating formula introduced by Guerra and Toninelli to investigate numerically the finite size corrections to the free energy of the Sherrington--Kirkpatrick model. The results are compatible with a $(1/12 N) \ln(N/N_0)$ behavior at $T_c$, as predicted by Parisi, Ritort and Slanina, and a $1/N^{2/3}$ behavior below $T_c$.