Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories

Abstract

We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry $S_q$ in $d=6-\epsilon$ (Landau-Potts field theories) and $d=4-\epsilon$ (hypertetrahedral models) up to three loops.We use our results to determine the $\epsilon$-expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and forests ($q\to 0$), and bond percolations ($q\to 1$). We also explicitly verify several expected degeneracies in the spectrum of relevant operators for natural values of $q$ upon analytic continuation, which are linked to logarithmic corrections of CFT correlators, and use the $\epsilon$-expansion to determine the universal coefficients of such logarithms.

15 pages, 3 tables, 3 figures; v2: improved version with estimates relevant for the cubic model, to appear in EPJC

References in corpus (8)

• Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
• Short-range correlations in percolation at criticality
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• The three-dimensional, three state Potts model in a negative external field
• Multi-critical multi-field models: a CFT approach to the leading order
• $N$-cluster correlations in four- and five-dimensional percolation
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Universal correlations in percolation

Cited by in corpus (3)

• The two upper critical dimensions of the Ising and Potts models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions