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

M. Safari; G. P. Vacca; O. Zanusso

doi:10.1140/epjc/s10052-020-08687-0

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2020) 80: 1127
https://doi.org/10.1140/epjc/s10052-020-08687-0

Regular Article – Theoretical Physics

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

M. Safari¹, G. P. Vacca² and O. Zanusso³^c

¹ Romanian Institute of Science and Technology, Str. Virgil Fulicea 3, 400022, Cluj-Napoca, Romania
² INFN-Sezione di Bologna, via Irnerio 46, 40126, Bologna, Italy
³ Università di Pisa and INFN-Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy

^c omar.zanusso@unipi.it

Received: 23 September 2020
Accepted: 17 November 2020
Published online: 7 December 2020

Abstract

We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry $S_{q}$ $$S_q$$ in $d = 6 - ϵ$ $d=6-\epsilon$ (Landau–Potts field theories) and $d = 4 - ϵ$ $d=4-\epsilon$ (hypertetrahedral models) up to three loops. We use our results to determine the $ϵ$ $\epsilon$ -expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and forests ( $q \to 0$ $q\rightarrow 0$ ), and bond percolations ( $q \to 1$ $q\rightarrow 1$ ). 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 $ϵ$ $\epsilon$ -expansion to determine the universal coefficients of such logarithms.

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© The Author(s) 2020

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