Frustration and Fluctuations in Systems with Quenched Disorder

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.