Probability and Mathematical Physics Seminar

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Structural analysis of Gibbs states and metastates in short-range classical spin glasses

Speaker: Nicholas Read, Yale University

Location: Warren Weaver Hall 1302

Date: Friday, March 7, 2025, 11:10 a.m.

Synopsis:

The old problem of the equilibrium spin systems with quenched disorder remains unsolved and controversial. Different points of view concern whether the equilibrium (Gibbs) states in the low-temperature spin-glass phase of a short-range system decompose into many ordered or ``pure'' states (as suggested by replica symmetry breaking theory (RSB)) or whether instead there are only one or two pure states, related by symmetry (the basis for the scaling-droplet theory). The question does not have much meaning in a finite size system, and so Gibbs states in infinite size are essential. To analyze infinite size, the concept of metastate (introduced by Aizenman, Wehr, Newman, and Stein) is essential. A metastate is a probability distribution on Gibbs states at given disorder, with certain properties. In this talk we describe recent progress in rigorous results on these systems; these results are in accord with, and certainly do not rule out, the predictions of RSB for short-range systems. The rigorous results include a new concept of decomposable metastates, and the result that any metastate can be decomposed into indecomposable metastates.  All results describe what is allowed in a metastate; existence questions of whether non-trivial Gibbs states actually occur will not be considered.