3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

TL;DR

This paper compares the statistical properties of the 3D spin glass and 2D XY models, revealing phase transition evidence in the former and Kosterlitz-Thouless behavior in the latter, emphasizing the importance of finite size effects.

Contribution

It provides a detailed comparison of the overlap distributions and Binder cumulants, highlighting the different phase transition mechanisms in the two models.

Findings

Evidence of phase transition in 3D spin glass via Binder cumulant crossing.

XY model behavior aligns with the Kosterlitz-Thouless scenario.

Finite size effects are crucial for accurate analysis.

Abstract

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyze similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behavior of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with by using great care in order to discern among two very different physical pictures that can look very similar if analyzed without large attention.