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

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