The self-consistent approach to the two-dimensional Ising model with quenched random bonds is extended to the full lattice theory described by four real fermions. A calculation of the averaged spin-spin correlation function for large separation of the spins in the disorder-dominated phase indicates an exponential decay of this quantity and therefore a vanishing spontaneous magnetization. The corresponding correlation length is proportional to 1/ eta 2 , where eta denotes the order parameter of the new phase introduced by Ziegler (1990).The self-consistent approach to the two-dimensional Ising model with quenched random bonds is extended to the full lattice theory described by four real fermions. A calculation of the averaged spin-spin correlation function for large separation of the spins in the disorder-dominated phase indicates an exponential decay of this quantity and therefore a vanishing spontaneous magnetization. The corresponding correlation length is proportional to 1/ eta 2 , where eta denotes the order parameter of the new phase introduced by Ziegler (1990).

arXiv:cond-mat/9310045Journal of Physics A Mathematical and GeneralDec 21, 19930 citations

Self-averaging and criticality: A comparative study in 2d random bond spin models

Nikolaos G. Fytas, Anastasios Malakis

We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple ferromagnetic Ising model are studied. We find that, the random bond SAF model shows a strong violation of self-averaging, much stronger than that observed in the case of the random bond Ising model. Our analysis of the asymptotic scaling behavior of the variance of the distribution of the sample-dependent pseudocritical temperatures is found to be consistent with the renormalization group prediction of Aharony and Harris. Using this alternative approach, we find estimates of the correlation length exponent $ν$ in agreement with results obtained from the usual finite-size scaling (FSS) methodology.We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple ferromagnetic Ising model are studied. We find that, the random bond SAF model shows a strong violation of self-averaging, much stronger than that observed in the case of the random bond Ising model. Our analysis of the asymptotic scaling behavior of the variance of the distribution of the sample-dependent pseudocritical temperatures is found to be consistent with the renormalization group prediction of Aharony and Harris. Using this alternative approach, we find estimates of the correlation length exponent $ν$ in agreement with results obtained from the usual finite-size scaling (FSS) methodology.

arXiv:0810.5438Oct 30, 20080 citations

ν

in agreement with results obtained from the usual finite-size scaling (FSS) methodology.