Random Energy Model at Complex Temperatures
D.B. Saakian
TL;DR
This paper maps the phase diagram of the Random Energy Model at complex temperatures and introduces a new analytical approach for studying zeroes of the statistical sum, extending to generalized models and finite-dimensional systems.
Contribution
It provides the complete phase diagram of REM at complex temperatures and proposes a novel analytical method for zeroes analysis applicable to GREM and finite-dimensional systems.
Findings
Density of zeroes for the statistical sum identified
Phase diagram of REM at complex temperatures mapped
New analytical method for zeroes in finite-dimensional systems proposed
Abstract
The complete phase diagram of Random Energy Model (REM) is obtained for complex temperatures using the method proposed by Derrida. We find the density of zeroes for statistical sum. Then the method is applied to Generalized Random Energy Model (GREM). This allows us to propose new analytical method for investigating zeroes of statistical sum for finite-dimensional systems.
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