Scaling Limits of Disorder Relevant Non-Binary Spin Systems

TL;DR

This paper extends existing criteria for binary spin systems with random fields to non-binary systems, providing insights into their scaling limits and disorder relevance.

Contribution

It generalizes the criteria for non-trivial continuum and weak disorder limits from binary to non-binary spin systems.

Findings

Extended criteria applicable to non-binary spin systems.

Identified conditions for non-trivial scaling limits.

Enhanced understanding of disorder relevance in complex spin models.

Abstract

In [7], Caravenna, Sun and Zygouras gave general criteria for the partition functions of binary valued spin systems with a relevant random field perturbation to have non-trivial continuum and weak disorder limits. In this work, we show how these criteria can be extended to non-binary valued spin systems.