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Wang–Landau study of the critical behavior of the bimodal 3D random field Ising model

Laura Hernández, Horacio Ceva

arXiv:cond-mat/0702398Physica A Statistical Mechanics and its ApplicationsJan 10, 200822 citations

Monte Carlo analysis of the critical properties of the two-dimensional randomly bond-diluted Ising model via Wang–Landau algorithm

Ioannis A. Hadjiagapiou

Physica A Statistical Mechanics and its ApplicationsDec 22, 201016 citations

Bond dilution in the 3D Ising model: a Monte Carlo study

Pierre Emmanuel Berche, Christophe Chatelain, Bertrand Berche +1 more

arXiv:cond-mat/0402596The European Physical Journal BApr 1, 200468 citations

Wang–Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions

Nikolaos G. Fytas, Anastasios Malakis, Ioannis Georgiou

We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor ( J nn ) and next-nearest-neighbor ( J nnn ) antiferromagnetic interactions. We consider the case R = J nn / J nnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor ( J nn ) and next-nearest-neighbor ( J nnn ) antiferromagnetic interactions. We consider the case R = J nn / J nnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.

arXiv:0804.4545Journal of Statistical Mechanics Theory and ExperimentJul 24, 20089 citations

Phase transition in the 2D Ising model with impurity bonds

Виктор Степанович Доценко, В. КИРИЛОВСКИЙ С

ZhETF Pisma RedaktsiiuJan 1, 19811 citation

Wang–Landau study of the 2d random-bond Blume–Capel model

Anastasios Malakis, A. Nihat Berker, Ioannis A. Hadjiagapiou +1 more

We study, via a two-stage Wang–Landau (WL) strategy, the random-bond version of the square lattice ferromagnetic Blume–Capel (BC) model, in both the first- and second-order phase transition regimes of the pure model. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with v=1.30(6) and β/v=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of 2d systems with and without quenched disorder.We study, via a two-stage Wang–Landau (WL) strategy, the random-bond version of the square lattice ferromagnetic Blume–Capel (BC) model, in both the first- and second-order phase transition regimes of the pure model. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with v=1.30(6) and β/v=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of 2d systems with and without quenched disorder.

Physics ProcediaFeb 1, 20100 citations

Wang-Landau study of the 3D Ising model with bond disorder

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