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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2006

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

Résumé

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 zero-temperature 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.
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Dates et versions

hal-00079515 , version 1 (13-06-2006)
hal-00079515 , version 2 (25-08-2006)

Identifiants

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Marco Picco, Andreas Honecker, Pierre Pujol. Strong disorder fixed points in the two-dimensional random-bond Ising model. Journal of Statistical Mechanics: Theory and Experiment, 2006, pp.P09006. ⟨10.1088/1742-5468/2006/09/P09006⟩. ⟨hal-00079515v2⟩
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