Functional RG approach to the Potts model

Abstract

The critical behavior of the $(n+1)$-states Potts model in $d$-dimensions is studied with functional renormalization group techniques. We devise a general method to derive $\beta$-functions for continuos values of $d$ and $n$ and we write the flow equation for the effective potential (LPA) when instead $n$ is fixed. We calculate several critical exponents, which are found to be in good agreement with Monte Carlo simulations and $\epsilon$-expansion results available in the literature. In particular, we focus on Percolation $(n\to 0)$ and Spanning Forest $(n\to -1)$ which are the only non-trivial universality classes in $d=4,5$ and where our methods converge faster.

References in corpus (6)

• Exact evolution equation for the effective potential
• Critical exponents of O(N) models in fractional dimensions
• Gauge-field-assisted Kekulé quantum criticality
• Scaling Solutions in Continuous Dimension
• Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
• Confinement in the q-state Potts field theory

Cited by in corpus (8)

• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Constraints on discrete global symmetries in quantum gravity
• Remarks on a melonic field theory with cubic interaction
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• The two upper critical dimensions of the Ising and Potts models
• Phase diagrams of lattice models on Cayley tree and chandelier network: a review
• Dualities between fermionic theories and the Potts model
• Renormalization of supersymmetric chiral theories in rational spacetime dimensions