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Parisi formula for balanced Potts spin glass by Bates, Erik; Sohn, Youngtak is a scholarly article available to read on EtoBox.

What is Parisi formula for balanced Potts spin glass about?

The Potts spin glass is a generalization of the Sherrington--Kirkpatrick (SK) model that allows for spins to take more than two values. Based on a novel synchronization mechanism, Panchenko (2018) showed that the limiting free energy is given by a Parisi-type variational formula. The functional order parameter in this formula is a probability measure on a monotone path in the space of positive-semidefinite matrices. By comparison, the order parameter for the SK model is much simpler: a probability measure on the unit interval. Nevertheless, a longstanding prediction by Elderfield and Sherrington (1983) is that the order parameter for the Potts spin glass can be reduced to that of the SK model. We prove this prediction for the balanced Potts spin glass, where the model is constrained so that the fraction of spins taking each value is asymptotically the same. It is generally believed that the limiting free energy of the balanced model is the same as that of the unconstrained model, in which case our results reduce the functional order parameter of Panchenko's variational formula to probability measures on the unit interval. The intuitive reason -- for both this belief and the Elderfi

Author

Bates, Erik; Sohn, Youngtak

Published

2023

Language

EN