The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: Entropy, universality, chaos and cascades in the renormalization group flow

TL;DR

This paper investigates the complex zero-temperature phases of 2D discrete spin glasses, focusing on entropy, chaos, and universality, using the Migdal-Kadanoff renormalization group to analyze fixed points and phase transitions.

Contribution

It reveals the connection between multiple zero-temperature phases, entropy fluctuations, and chaos through the analysis of a cascade of fixed points in the renormalization group flow.

Findings

Identification of two unstable fixed points corresponding to distinct spin-glass phases

Demonstration of the role of entropy fluctuations and temperature chaos

Insights into universality in the behavior of 2D spin glasses

Abstract

The properties of discrete two-dimensional spin glasses depend strongly on the way the zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal-Kadanoff renormalization group. We see, in particular, how these properties are connected with the presence of a cascade of fixed points in the renormalization group flow. Of particular interest are two unstable fixed points that correspond to two different spin-glass phases at zero temperature. We discuss how these phenomena are related with the presence of entropy fluctuations and temperature chaos, and universality in this model.