A constrained Potts antiferromagnet model with an interface representation

TL;DR

This paper introduces a constrained four-state Potts model on a square lattice, mapping spin configurations to a high-dimensional interface, and investigates its critical behavior through Monte Carlo simulations, revealing anomalous height fluctuations.

Contribution

It proposes a novel constrained Potts model with specific interface mapping and analyzes its critical properties, highlighting a potential smooth phase with long-range order.

Findings

Height fluctuations show anomalous wavevector dependence

Results suggest the presence of a smooth phase with long-range order

Monte Carlo simulations indicate non-standard critical behavior

Abstract

We define a four-state Potts model ensemble on the square lattice, with the constraints that neighboring spins must have different values, and that no plaquette may contain all four states. The spin configurations may be mapped into those of a 2-dimensional interface in a 2+5 dimensional space. If this interface is in a Gaussian rough phase (as is the case for most other models with such a mapping), then the spin correlations are critical and their exponents can be related to the stiffness governing the interface fluctuations. Results of our Monte Carlo simulations show height fluctuations with an anomalous dependence on wavevector, intermediate between the behaviors expected in a rough phase and in a smooth phase; we argue that the smooth phase (which would imply long-range spin order) is the best interpretation.