Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach. (English) Zbl 07906144
Summary: 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 et al., 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.
MSC:
| 82Bxx | Equilibrium statistical mechanics |
| 82Dxx | Applications of statistical mechanics to specific types of physical systems |
| 82Cxx | Time-dependent statistical mechanics (dynamic and nonequilibrium) |
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