# Study of longitudinal fluctuations of the Sherrington-Kirkpatrick model

## TL;DR

This paper investigates the finite-size corrections to the free energy of the Sherrington-Kirkpatrick spin glass model at low temperatures, focusing on longitudinal fluctuations and estimating the correction exponent.

## Contribution

It provides an analytical and numerical estimate of the correction exponent =0.8 for the model, emphasizing the role of longitudinal fluctuations.

## Key findings

- The correction exponent  is approximately 0.8.
- Longitudinal fluctuations significantly influence finite-size corrections.
- Analytical and numerical methods agree on the estimate.

## Abstract

We study finite-size corrections to the free energy of the Sherrington-Kirkpatrick spin glass in the low temperature phase. We investigate the role of longitudinal fluctuations in these corrections, neglecting the transverse contribution. In particular, we are interested in the exponent $\alpha$ defined by the relation $f-f_\infty\sim N^{-\alpha}$. We perform both an analytical and numerical estimate of the analytical result for $\alpha$. From both the approaches we get the result: $\alpha=0.8$.