Higher moments of spin-spin correlation functions for the ferromagnetic random bond Potts model

TL;DR

This paper uses conformal field theory to compute higher moments of spin-spin correlation functions in the ferromagnetic random bond Potts model, extending previous work and providing bounds on the validity of the expansion.

Contribution

It generalizes previous calculations to higher moments and analyzes the validity range of the perturbative expansion in the three-state case.

Findings

Explicit dependence of correlation functions on p

Perturbative calculations up to second order in epsilon

Validity of expansion limited to p<=4 in the three-states case

Abstract

Using CFT techniques, we compute the disorder-averaged p-th power of the spin-spin correlation function for the ferromagnetic random bonds Potts model. We thus generalize the calculation of Dotsenko, Dotsenko and Picco, where the case p=2 was considered. Perturbative calculations are made up to the second order in epsilon (epsilon being proportional to the central charge deviation of the pure model from the Ising model value). The explicit dependence of the correlation function on $p$ gives an upper bound for the validity of the expansion, which seems to be valid, in the three-states case, only if p<=4.