Frustration and Fluctuations in Systems with Quenched Disorder

TL;DR

This paper reviews the concept of frustration in disordered systems, discusses the challenges in bounding free energy fluctuations, and highlights recent findings that these fluctuations scale with the square root of volume, offering insights into spin glass physics.

Contribution

It provides a historical overview of efforts to bound free energy fluctuations and discusses recent results on their scaling behavior in spin glasses.

Findings

Free energy fluctuations may scale as the square root of volume.

Upper bounds on fluctuations have been established, lower bounds are more challenging.

The Anderson conception of frustration offers a promising approach to unresolved issues in spin glass physics.

Abstract

As Phil Anderson noted long ago, frustration can be generally defined by measuring the fluctuations in the coupling energy across a plane boundary between two large blocks of material. Since that time, a number of groups have studied the free energy fluctuations between (putative) distinct spin glass thermodynamic states. While upper bounds on such fluctuations have been obtained, useful lower bounds have been more difficult to derive. I present a history of these efforts, and briefly discuss recent work showing that free energy fluctuations between certain classes of distinct thermodynamic states (if they exist) scale as the square root of the volume. The perspective offered here is that the power and generality of the Anderson conception of frustration suggests a potential approach toward resolving some longstanding and central issues in spin glass physics.