Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena

TL;DR

This paper introduces new quasiorder parameters for Potts models that, when combined with machine learning, effectively identify critical points and exponents, bridging the gap between ML models trained on Ising data and critical phenomena in Potts systems.

Contribution

It identifies alternative order parameters for Potts models that, together with ML insights, reveal critical behavior using reduced spin representations, expanding understanding of phase transitions.

Findings

Alternative order parameters accurately determine critical temperatures.

Reduced spin representations encode essential critical information.

Relationships between quasiorder parameters elucidate criticality mechanisms.

Abstract

Machine-learning (ML) models trained on Ising spin configurations have demonstrated surprising effectiveness in classifying phases of Potts models, even when processing severely reduced representations that retain only two spin states. To unravel this remarkable capability, we identify a family of alternative order parameters for the $q=3$ and $q=4$ Potts models on a square lattice, constructed from the occupancies of secondary and minimal spin states rather than the conventional dominant-state order parameter. Through systematic finite-size scaling analyses, we demonstrate that these quantities, along with a magnetization-like quantity derived from a reduced spin representation, accurately capture critical behavior, yielding critical temperatures and exponents consistent with established theoretical predictions and numerical benchmarks. Furthermore, we rigorously establish the fundamental relationships between these alternative (quasi)order parameters, demonstrating how they collectively encode criticality through different aspects of spin configurations. Our results clarify, within this specific setting, how reduced spin representations can retain the essential thermodynamic information needed for identifying critical behavior. Taken together, this work establishes a concrete bridge between Ising-trained ML models and critical phenomena in Potts systems by showing that Potts criticality can be encoded in more compact, non-traditional forms, thereby opening avenues for discovering analogous order parameters in broader spin systems.