Strong disorder fixed points in the two-dimensional random-bond Ising model

The random-bond Ising model on the square lattice has several disordered critical points, depending on the probability distribution of the bonds. There are a finite-temperature multicritical point, called Nishimori point, and a zerotemperature fixed point, for both a binary distribution where the coupling constants take the values ±J and a Gaussian disorder distribution. Inclusion of dilution in the ±J distribution (J = 0 for some bonds) gives rise to another zero-temperature fixed point which can be identified with percolation in the non-frustrated case (J ≥ 0). We study these fixed points using numerical (transfer matrix) methods. We determine the location, critical exponents, and central charge of the different fixed points and study the spin-spin correlation functions. Our main findings are the following: (1) We confirm that the Nishimori point is universal with respect to the type of disorder, i.e. we obtain the same central charge and critical exponents for the±J and Gaussian distributions of disorder. (2) The Nishimori point, the zero-temperature fixed point for the ±J and Gaussian distributions of disorder, and the percolation point in the diluted case all belong to mutually distinct universality classes. (3) The paramagnetic phase is re-entrant below the Nishimori point, i.e. the zero-temperature fixed points are not located exactly below the Nishimori point, neither for the ±J distribution, nor for the Gaussian distribution. PACS numbers: 75.50.Lk, 05.50.+q, 64.60.Fr Unité mixte de recherche du CNRS UMR 7589. Unité mixte de recherche du CNRS UMR 5672 associée à l’Ecole Normale Supérieure de Lyon.