We apply numerical simulations to study the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio $Γ^+/Γ^-$ for the magnetic susceptibility critical amplitudes. Our estimate $Γ^+/Γ^- = 1.67 \pm 0.15$ is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.We apply numerical simulations to study the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio $Γ^+/Γ^-$ for the magnetic susceptibility critical amplitudes. Our estimate $Γ^+/Γ^- = 1.67 \pm 0.15$ is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.

arXiv:cond-mat/0501291Condensed Matter PhysicsJan 1, 200518 citations

Monte Carlo simulations of Ising models

Walter Selke

Computer Physics CommunicationsAug 1, 19961 citation

Machine Learning of the Two-Dimensional Diluted Bond Ising Model

Nguyen Trong Luu, Pham Long Nhat, Nguyen Vo Nguyen Huy +7 more

The bond-diluted 2D Ising model is essential for understanding the effects of disorder on magnetic systems. Although the T-p phase diagram of this model has been developed through analytical methods and Monte Carlo simulations, the region near the percolation threshold pc remains insufficiently explored. In this study, we reinvestigate the impact of bond dilution on phase transitions in the bond-diluted 2D Ising model using a machine learning approach. A convolutional neural network, initially trained on data from the pure (undiluted) 2D Ising model, is employed through transfer learning to analyze bond-diluted systems. The numerical results show that as bond concentration decreases, the critical temperature also decreases, in agreement with previous Monte Carlo simulation results. Moreover, these findings are instrumental in estimating the critical bond dilution near the percolation threshold pc. As a result, a comprehensive phase diagram for the bond-diluted 2D Ising model has been constructed.The bond-diluted 2D Ising model is essential for understanding the effects of disorder on magnetic systems. Although the T-p phase diagram of this model has been developed through analytical methods and Monte Carlo simulations, the region near the percolation threshold pc remains insufficiently explored. In this study, we reinvestigate the impact of bond dilution on phase transitions in the bond-diluted 2D Ising model using a machine learning approach. A convolutional neural network, initially trained on data from the pure (undiluted) 2D Ising model, is employed through transfer learning to analyze bond-diluted systems. The numerical results show that as bond concentration decreases, the critical temperature also decreases, in agreement with previous Monte Carlo simulation results. Moreover, these findings are instrumental in estimating the critical bond dilution near the percolation threshold pc. As a result, a comprehensive phase diagram for the bond-diluted 2D Ising model has been constructed.

VNU Journal of Science Mathematics - PhysicsJul 30, 20250 citations

Monte Carlo simulations for two-dimensional Ising system far from equilibrium

XiaoWei Lei, Ji Zheng, Xiaoyu Zhao

Chinese Science BulletinFeb 1, 20076 citations

Γ^+/Γ^-

for the magnetic susceptibility critical amplitudes. Our estimate

Γ^+/Γ^- = 1.67 \pm 0.15

is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.