A multicritical Landau-Potts field theory

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.

12 pages, 5 figures; v2: improved discussion for the q=0 limit, to appear in PRD

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• The search for the universality class of metric quantum gravity
• The tricritical Ising CFT and conformal bootstrap
• The two upper critical dimensions of the Ising and Potts models
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• Anomalous Dimensions in Hypercubic Theories
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories