Strong disorder fixed points in the two-dimensional random-bond Ising model
| dc.creator | Picco, Marco | |
| dc.creator | Honecker, Andreas | |
| dc.creator | Pujol, Pierre | |
| dc.date | 2006-06-13 | |
| dc.date | 2006-08-25 | |
| dc.date.accessioned | 2026-07-07T07:12:36Z | |
| dc.date.available | 2026-07-07T07:12:36Z | |
| dc.description | 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. | |
| dc.description | final version to appear in JSTAT; minor changes | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0606312 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0606312 | |
| dc.identifier | Journal of Statistical Mechanics: Theory and Experiment (2006) P09006 | |
| dc.identifier | doi:10.1088/1742-5468/2006/09/P09006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112132 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Strong disorder fixed points in the two-dimensional random-bond Ising model | |
| dc.type | text |