Article Dans Une Revue SciPost Physics Année : 2023

Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach

Résumé

In this paper we provide new analytic results on two-dimensional $q$-Potts models ($q \geq 2$) in the presence of bond disorder correlations which decay algebraically with distance with exponent $a$. In particular, our results are valid for the long-range bond disordered Ising model ($q=2$). We implement a renormalization group perturbative approach based on conformal perturbation theory. We extend to the long-range case the RG scheme used in [V. Dotsenko, Nucl. Phys. B 455 701 23] for the short-range disorder. Our approach is based on a $2$-loop order double expansion in the positive parameters $(2-a)$ and $(q-2)$. We will show that the Weinrib-Halperin conjecture for the long-range thermal exponent can be violated for a non-Gaussian disorder. We compute the central charges of the long-range fixed points finding a very good agreement with numerical measurements.

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hal-04135656 , version 1 (05-07-2023)

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Francesco Chippari, Marco Picco, Raoul Santachiara. Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach. SciPost Physics, 2023, 15 (4), pp.135. ⟨10.21468/SciPostPhys.15.4.135⟩. ⟨hal-04135656⟩
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