Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nuclear Physics B

Monte Carlo study of the 2D Ising model with impurities

V. B. Andreǐchenko, Vl.S. Dotsenko, Walter Selke, Jian‐Sheng Wang

Published Nov 1, 1990• 68 citations
Publisher
DOI
10.1016/0550-3213(90)90669-5

Related papers

Monte Carlo Renormalization Group of Dilute 2D Ising Dynamics

Vladimir V. Prudnikov, O. N. Markov

The critical relaxation of the magnetization in a 2D Ising model with quenched random non-magnetic impurities is studied by numerical simulation. A square lattice of size 400 2 and spin concentrations p = 1.0, 0.95, 0.9, 0.85, 0.8, 0.75 and 0.7 are considered. The dynamical critical exponent z is determined by the dynamical renormalization group Monte Carlo method. The values for z(p) are: z (1) = 2.24 ± 0.07, z (0.95) = 2.24 ± 0.06, z (0.9) = 2.24 ± 0.06, z (0.85) = 2.38 ± 0.05, z (0.8) = 2.51 ± 0.06, z (0.75) = 2.66 ± 0.07 and z (0.7) = 2.88 ± 0.06. A singular dynamic-scaling behaviour with z(p) = A '|ln( p − p c )| + B ' is found for systems with spin concentrations near the percolation threshold p c , where A ' = 0.56 ± 0.07 and B ' = 1.62 ± 0.07 are temperature-independent constants.

Europhysics Letters (EPL)•Jan 20, 1995•16 citations

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

XiaoWei Lei, Ji Zheng, Xiaoyu Zhao

Chinese Science Bulletin•Feb 1, 2007•6 citations

Critical-Point Correlation Function for the 2D Random Bond Ising Model

A. L Talapov, Щур Лев Николаевич

High-accuracy Monte Carlo simulation results for a 1024 * 1024 Ising system with ferromagnetic impurity bonds are presented. The spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since the critical temperature for the system with impurities is almost two times lower than pure Ising T c . Finite corrections to the correlation function due to combined action of impurities and finite lattice size are described.

arXiv:hep-lat/9404002•Europhysics Letters (EPL)•Jul 20, 1994•30 citations

Phase transition in the 2D Ising model with impurity bonds

Виктор Степанович Доценко, В. КИРИЛОВСКИЙ С

ZhETF Pisma Redaktsiiu•Jan 1, 1981•1 citation

Monte Carlo simulations of Ising models

Walter Selke

Computer Physics Communications•Aug 1, 1996•1 citation

Critical Behavior of the Randomly Spin Diluted 2D Ising Model: A Grand Ensemble Approach

Reimer Kühn

The critical behavior of the 2D spin diluted Ising model is investigated by a new method that combines a grand ensemble approach to disordered systems with phenomenological renormalization. We observe a continuous variation of critical exponents with the density $\ensuremath{\rho}$ of magnetic impurities, respecting, however, weak universality in the sense that $\ensuremath{\eta}$ and $\frac{\ensuremath{\gamma}}{\ensuremath{\nu}}$ do not depend on $\ensuremath{\rho}$ while $\ensuremath{\gamma}$ and $\ensuremath{\nu}$ separately do. Our results are in complete agreement with a recent Monte Carlo study.

arXiv:cond-mat/9405047•Physical Review Letters•Oct 17, 1994•62 citations
The critical relaxation of the magnetization in a 2D Ising model with quenched random non-magnetic impurities is studied by numerical simulation. A square lattice of size 400 2 and spin concentrations p = 1.0, 0.95, 0.9, 0.85, 0.8, 0.75 and 0.7 are considered. The dynamical critical exponent z is determined by the dynamical renormalization group Monte Carlo method. The values for z(p) are: z (1) = 2.24 ± 0.07, z (0.95) = 2.24 ± 0.06, z (0.9) = 2.24 ± 0.06, z (0.85) = 2.38 ± 0.05, z (0.8) = 2.51 ± 0.06, z (0.75) = 2.66 ± 0.07 and z (0.7) = 2.88 ± 0.06. A singular dynamic-scaling behaviour with z(p) = A '|ln( p − p c )| + B ' is found for systems with spin concentrations near the percolation threshold p c , where A ' = 0.56 ± 0.07 and B ' = 1.62 ± 0.07 are temperature-independent constants.
The critical behavior of the 2D spin diluted Ising model is investigated by a new method that combines a grand ensemble approach to disordered systems with phenomenological renormalization. We observe a continuous variation of critical exponents with the density $\ensuremath{\rho}$ of magnetic impurities, respecting, however, weak universality in the sense that $\ensuremath{\eta}$ and $\frac{\ensuremath{\gamma}}{\ensuremath{\nu}}$ do not depend on $\ensuremath{\rho}$ while $\ensuremath{\gamma}$ and $\ensuremath{\nu}$ separately do. Our results are in complete agreement with a recent Monte Carlo study.