Duality in finite-dimensional spin glasses

TL;DR

This paper investigates the precise location of the multicritical point in finite-dimensional spin glasses, linking duality, the replica method, and analyticity assumptions to refine the theoretical understanding of phase transitions.

Contribution

It clarifies the mathematical basis of a previously used ansatz by relating it to the analyticity of a specific function, improving the theoretical framework for spin glass phase diagrams.

Findings

Conjecture on the exact multicritical point location agrees with numerical results.

The ansatz is shown to be connected to the analyticity of a certain function.

Provides a clearer mathematical understanding of duality in spin glasses.

Abstract

We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function.