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arXiv · 2009.02589

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

Mahmoud Safari·Gian Paolo Vacca·Omar Zanusso
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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 ($q\to0$), and bond percolations ($q\to1$). 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.

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Mahmoud Safari, Gian Paolo Vacca, Omar Zanusso. 2020-09-05. Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories. https://doi.org/10.1140/epjc%2Fs10052-020-08687-0

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