Our method uses topological properties of the large clusters in the single-cluster algorithm of Wolff for Monte Carlo simulations of spin systems. We have applied this method to the d=3 Ising model with film geometry near the special transition. As a test for the method we determined the bulk critical temperature and the critical indices in fair agreement with the results obtained by other methods. The new results refer to the critical surface coupling ${\mathit{J}}_{1\mathit{c}}$ /J=1.5004(20) and the surface exponents, where \ensuremath{\varphi}=0.461(15) and ${\mathrm{\ensuremath{\beta}}}_{\mathit{i}}^{\mathit{m}}$=0.237(5).Our method uses topological properties of the large clusters in the single-cluster algorithm of Wolff for Monte Carlo simulations of spin systems. We have applied this method to the d=3 Ising model with film geometry near the special transition. As a test for the method we determined the bulk critical temperature and the critical indices in fair agreement with the results obtained by other methods. The new results refer to the critical surface coupling ${\mathit{J}}_{1\mathit{c}}$/J=1.5004(20) and the surface exponents, where \ensuremath{\varphi}=0.461(15) and ${\mathrm{\ensuremath{\beta}}}_{\mathit{i}}^{\mathit{m}}$=0.237(5).

Physical Review LettersOct 26, 199243 citations

Computer investigations of the three-dimensional Ising model

Michael J. Creutz, P. Mitra, Kevin J. M. Moriarty

Journal of Statistical PhysicsMar 1, 198610 citations

Critical parameters for thed=3 Ising model in a film geometry

C. Ruge, Friedrich Wagner

We simulated the critical behavior of the d=3 Ising model with surfaces with a cluster Monte Carlo method at the multicritical point and at the ordinary transition. The surface exponents ${\mathrm{\ensuremath{\beta}}}_{1}$ have been determined using finite-size scaling. The errors of the resulting values ${\mathrm{\ensuremath{\beta}}}_{1}^{\mathit{m}}$=0.2375(15) and ${\mathrm{\ensuremath{\beta}}}_{1}^{0}$=0.807(4) are an order of magnitude smaller than in previous determinations. Whereas the values of the exponents agree with the prediction of the \ensuremath{\epsilon} expansion, the universal ratios of susceptibility and magnetization amplitudes at the special transition are at variance with those predictions.We simulated the critical behavior of the d=3 Ising model with surfaces with a cluster Monte Carlo method at the multicritical point and at the ordinary transition. The surface exponents ${\mathrm{\ensuremath{\beta}}}_{1}$ have been determined using finite-size scaling. The errors of the resulting values ${\mathrm{\ensuremath{\beta}}}_{1}^{\mathit{m}}$=0.2375(15) and ${\mathrm{\ensuremath{\beta}}}_{1}^{0}$=0.807(4) are an order of magnitude smaller than in previous determinations. Whereas the values of the exponents agree with the prediction of the \ensuremath{\epsilon} expansion, the universal ratios of susceptibility and magnetization amplitudes at the special transition are at variance with those predictions.

Physical review. B, Condensed matterAug 1, 199529 citations

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

Alan M. Ferrenberg, Jiahao Xu, David Paul Landau

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 16^{3} to 1024^{3}. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature K_{c}=0.221654626(5) and the critical exponent of the correlation length ν=0.629912(86) with precision that exceeds all previous Monte Carlo estimates.While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 16^{3} to 1024^{3}. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature K_{c}=0.221654626(5) and the critical exponent of the correlation length ν=0.629912(86) with precision that exceeds all previous Monte Carlo estimates.

arXiv:1806.03558Physical review. EApr 4, 2018191 citations

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Hans-Otto Heuer

Journal of Statistical PhysicsAug 1, 199312 citations

{\mathit{J}}_{1\mathit{c}}

/J=1.5004(20) and the surface exponents, where \ensuremath{\varphi}=0.461(15) and ${\mathrm{\ensuremath{\beta}}}_{\mathit{i}}^{\mathit{m}}$=0.237(5).