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

by Francesco Chippari, Marco Picco, Raoul Santachiara

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Submission summary

Authors (as registered SciPost users): Francesco Chippari · Raoul Santachiara
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-08-21
Date submitted: 2023-08-09 16:15
Submitted by: Chippari, Francesco
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


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.

Published as SciPost Phys. 15, 135 (2023)

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