Spin glasses in the limit of an infinite number of spin components

TL;DR

This paper investigates the behavior of spin glasses with an infinite number of spin components, revealing zero order parameter, quasi long-range order, and a zero transition temperature in three dimensions.

Contribution

It provides a detailed analysis of the infinite-component limit in spin glasses, showing the absence of conventional order and the presence of quasi long-range correlations.

Findings

Order parameter is zero in the infinite-component limit

Quasi long-range order exists below transition temperature

Transition temperature is zero in three dimensions

Abstract

We consider the spin glass model in which the number of spin components, m, is infinite. In the formulation of the problem appropriate for numerical calculations proposed by several authors, we show that the order parameter defined by the long-distance limit of the correlation functions is actually zero and there is only "quasi long range order" below the transition temperature. We also show that the spin glass transition temperature is zero in three dimensions.