Dynamical Probability Distribution Function of the SK Model at High Temperatures

TL;DR

This paper derives an explicit time-dependent probability distribution for the SK spin glass model at high temperatures, revealing deviations from previous theoretical assumptions and providing formulas for macroscopic quantities after temperature changes.

Contribution

It presents a third-order high-temperature expansion of the probability distribution function for the SK model, challenging prior assumptions and offering explicit time-dependent expressions.

Findings

Deviation from Coolen, Laughton, and Sherrington's theory

Quantitative estimates of theory deviations

Explicit formulas for macroscopic quantities after temperature shifts

Abstract

The microscopic probability distribution function of the Sherrington-Kirkpatrick (SK) model of spin glasses is calculated explicitly as a function of time by a high-temperature expansion. The resulting formula to the third order of the inverse temperature shows that an assumption made by Coolen, Laughton and Sherrington in their recent theory of dynamics is violated. Deviations of their theory from exact results are estimated quantitatively. Our formula also yields explicit expressions of the time dependence of various macroscopic physical quantities when the temperature is suddenly changed within the high-temperature region.