A multicritical Landau-Potts field theory

TL;DR

This paper introduces a renormalizable Landau-Potts field theory with multicritical behavior, potentially extending critical models of percolation and spanning clusters to three dimensions, and explores phase transition separations.

Contribution

It presents a new multicritical Landau-Potts field theory with potential applications to percolation models and phase transition analysis in three dimensions.

Findings

Hints at multicritical generalizations of spanning cluster models.

Discusses phase separation in the Potts model diagram.

Provides a perturbative renormalization analysis.

Abstract

We investigate a perturbatively renormalizable $S_{q}$ invariant model with $N=q-1$ scalar field components below the upper critical dimension $d_c=\frac{10}{3}$. Our results hint at the existence of multicritical generalizations of the critical models of spanning random clusters and percolations in three dimensions. We also discuss the role of our multicritical model in a conjecture that involves the separation of first and second order phases in the $(d,q)$ diagram of the Potts model.