Overlap Structure and Free Energy Fluctuations in Short-Range Spin Glasses

Author:

C. M. Newman, D. L. Stein

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistical Mechanics (cond-mat.stat-mech), Mathematical Physics (math-ph)

journal:

date:

2023-06-11 16:00:00

Abstract

We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on Gibbs states whose edge overlap values with a reference state fall within a specified range. Using this metastate we show that, in any dimension, the variance of free energy difference fluctuations between pure states within a single mixed Gibbs state with multiple edge overlap values diverges linearly with the volume. This conclusion would be avoided if the distribution of edge overlap values in any mixed Gibbs state has at most two values: the self-overlap and an overlap between non-spin-flip related states at a smaller value, as occurs in one-step replica symmetry breaking. We discuss some implications of these results.

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