Physical review. B, Condensed matter

Monte Carlo studies of universal critical amplitudes for the three-dimensional Ising model: Correlation length and renormalized coupling

Pik-Yin Lai, K. K. Mon

Published Dec 1, 1989• 6 citations

Abstract

We report Monte Carlo studies of the finite-size second-moment correlation length and renormalized coupling at criticality for the three-dimensional Ising model on body-centered-cubic lattices. The related finite-size scaling amplitudes are estimated and compared with the simple-cubic lattice results of recent extensive simulations. The amplitudes agreed within statistical uncertainty and are consistent with finite-size-scaling arguments for universality.

DOI: 10.1103/physrevb.40.11120

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Physical review. B, Condensed matter

Monte Carlo studies of universal critical amplitudes for the three-dimensional Ising model: Correlation length and renormalized coupling

Pik-Yin Lai, K. K. Mon

Published Dec 1, 1989• 6 citations

Publisher

Abstract

DOI: 10.1103/physrevb.40.11120

Related papers

Surface free energies of three-dimensional Ising models and universality of finite-size scaling amplitudes by direct Monte Carlo sampling

K. K. Mon, M. P. Nightingale

Physical review. B, Condensed matterMay 1, 198516 citations

Monte Carlo studies of correlation length and hyperscaling in the three-dimensional Ising model

Pik-Yin Lai, K. K. Mon

We report extensive Monte Carlo simulations and finite-size scaling analysis of the correlation length (${\ensuremath{\xi}}_{\mathrm{L}}$) for the spin-spin correlation function and the renormalized coupling ( ${\mathrm{g}}_{\mathrm{L}}$ ) of the simple-cubic Ising model with a wide range of lattice sizes (L\ensuremath{\le}96). New methods of analysis which avoid assumptions related to the correlation length were introduced. The exponents \ensuremath{\nu} and 2-\ensuremath{\alpha} were estimated from separate analysis of ${\ensuremath{\xi}}_{\mathrm{L}}$ and ${\mathrm{g}}_{\mathrm{L}}$ , respectively. A value of ${\mathrm{\ensuremath{\omega}}}^{\mathrm{*}}$\ensuremath{\approxeq}0.001\ifmmode\pm\else\textpm\fi{}0.07 for the Fisher exponent is obtained. This is consistent with a very small or no violations of hyperscalings.We report extensive Monte Carlo simulations and finite-size scaling analysis of the correlation length (${\ensuremath{\xi}}_{\mathrm{L}}$) for the spin-spin correlation function and the renormalized coupling (${\mathrm{g}}_{\mathrm{L}}$) of the simple-cubic Ising model with a wide range of lattice sizes (L\ensuremath{\le}96). New methods of analysis which avoid assumptions related to the correlation length were introduced. The exponents \ensuremath{\nu} and 2-\ensuremath{\alpha} were estimated from separate analysis of ${\ensuremath{\xi}}_{\mathrm{L}}$ and ${\mathrm{g}}_{\mathrm{L}}$, respectively. A value of ${\mathrm{\ensuremath{\omega}}}^{\mathrm{*}}$\ensuremath{\approxeq}0.001\ifmmode\pm\else\textpm\fi{}0.07 for the Fisher exponent is obtained. This is consistent with a very small or no violations of hyperscalings.

Physical Review LettersMay 29, 198912 citations

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Critical finite-size-scaling amplitudes of a fully anisotropic three-dimensional Ising model

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A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders n\ifmmode\times\else\texttimes\fi{}n\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty} is investigated by the transfer-matrix finite-size-scaling method. In addition to the previously obtained critical amplitudes of the inverse correlation lengths and singular part of the free energy [M. A. Yurishchev, Phys. Rev. B 50, 13 533 (1994)], the amplitudes of the usual (``linear'') and nonlinear susceptibilities and the amplitude of the second derivative of the spin-spin inverse correlation length with respect to the external field are calculated. The behavior of critical amplitude combinations (which, in accordance with the Privman-Fisher equations, do not contain in their composition the nonuniversal metric coefficients and geometry prefactor) are studied as a function of the interaction anisotropy parameters. A universality domain for the amplitude ratios is found in the quasi-one-dimensional regime of interactions in the system. In the case of a fully isotropic three-dimensional Ising model for which the high precision values of the critical coupling and critical-point free energy are available, improved estimates are obtained for the following four universal quantities: (1) the amplitude of spin-spin inverse correlation length, (2) the amplitude of singular part of the free energy, (3) the ratio of the amplitude of a second derivative of the spin-spin inverse correlation length with respect to the external field to the usual susceptibility amplitude, and (4) the ratio of the nonlinear susceptibility amplitude to the square of the linear susceptibility amplitude (i.e., for the finite-size counterpart of the four-point renormalized coupling constant).A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders n\ifmmode\times\else\texttimes\fi{}n\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty} is investigated by the transfer-matrix finite-size-scaling method. In addition to the previously obtained critical amplitudes of the inverse correlation lengths and singular part of the free energy [M. A. Yurishchev, Phys. Rev. B 50, 13 533 (1994)], the amplitudes of the usual (``linear'') and nonlinear susceptibilities and the amplitude of the second derivative of the spin-spin inverse correlation length with respect to the external field are calculated. The behavior of critical amplitude combinations (which, in accordance with the Privman-Fisher equations, do not contain in their composition the nonuniversal metric coefficients and geometry prefactor) are studied as a function of the interaction anisotropy parameters. A universality domain for the amplitude ratios is found in the quasi-one-dimensional regime of interactions in the system. In the case of a fully isotropic three-dimensional Ising model for which the high precision values of the critical coupling and critical-point free energy are available, improved estimates are obtained for the following four universal quantities: (1) the amplitude of spin-spin inverse correlation length, (2) the amplitude of singular part of the free energy, (3) the ratio of the amplitude of a second derivative of the spin-spin inverse correlation length with respect to the external field to the usual susceptibility amplitude, and (4) the ratio of the nonlinear susceptibility amplitude to the square of the linear susceptibility amplitude (i.e., for the finite-size counterpart of the four-point renormalized coupling constant).

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arXiv:cond-mat/9509016Journal of Physics A Mathematical and GeneralNov 21, 1995308 citations

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

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Physics of the Solid StateJun 1, 200519 citations

{\mathrm{g}}_{\mathrm{L}}

) of the simple-cubic Ising model with a wide range of lattice sizes (L\ensuremath{\le}96). New methods of analysis which avoid assumptions related to the correlation length were introduced. The exponents \ensuremath{\nu} and 2-\ensuremath{\alpha} were estimated from separate analysis of ${\ensuremath{\xi}}_{\mathrm{L}}$ and

{\mathrm{g}}_{\mathrm{L}}

, respectively. A value of ${\mathrm{\ensuremath{\omega}}}^{\mathrm{*}}$\ensuremath{\approxeq}0.001\ifmmode\pm\else\textpm\fi{}0.07 for the Fisher exponent is obtained. This is consistent with a very small or no violations of hyperscalings.