Construction and purpose of effective field theories for frustrated magnetic order

TL;DR

This paper reviews recent progress in understanding frustrated magnetic order through effective field theories, focusing on replica symmetry breaking in spin glass models like SK, revealing critical phenomena without traditional phase transitions.

Contribution

It introduces construction principles for effective field theories of frustrated magnetic systems, emphasizing the role of replica symmetry breaking and its complex physical effects.

Findings

Replica symmetry breaking leads to critical phenomena at low temperatures.

Effective field theories can be constructed from numerical data.

RSB explains glassy antiferromagnetic order phenomena.

Abstract

This article reviews recent years' progress in the low temperature analysis of standard models of spin glass order such as the Sherrington-Kirkpatrick (SK) model. Applications to CdTe/CdMnTe layered systems and explanation of glassy antiferromagnetic order at lowest temperatures stimulated us to study in detail the beautifully complex physical effects of replica symmetry breaking (RSB).We discuss analytical ideas based on highly precise numerical data which lead to the construction of relatively simple effective field theories for the SK model and help to understand the mysterious features of its exact solution. The goal is to find construction principles for the theory of interplay between frustrated magnetic order and various relevant physical degrees of freedom. The emphasis in this article is on the role of Parisi's RSB, which surprisingly creates critical phenomena in the low temperature limit despite the absence of a standard phase transition.