Lack of monotonicity in spin glass correlation functions

TL;DR

This paper investigates how correlation functions in spin glass systems behave under rescaling and volume changes, revealing violations of monotonicity that are present in ferromagnets but absent in spin glasses.

Contribution

It demonstrates that unlike ferromagnets, spin glass correlation functions do not exhibit monotonicity with respect to volume or interaction rescaling.

Findings

Correlation functions in spin glasses violate monotonicity.

Ferromagnets show monotonic increase in correlation functions.

Numerical evidence supports non-monotonic behavior in spin glasses.

Abstract

We study the response of a spin glass system with respect to the rescaling of its interaction random variables and investigate numerically the behaviour of the correlation functions with respect to the volume. While for a ferromagnet the local energy correlation functions increase monotonically with the scale and, by consequence, with respect to the volume of the system we find that in a general spin glass model those monotonicities are violated.