SciPost Submission Page
Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach
by Francesco Chippari, Marco Picco, Raoul Santachiara
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint Link: |
https://arxiv.org/abs/2306.01887v2
(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 |
| Specialties: |
- Statistical and Soft Matter Physics
|
| Approaches: |
Theoretical, Computational |
Abstract
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.
