Spin-dynamics simulations have been used to investigate the dynamic behavior of RbMnF_3, treating it as a classical Heisenberg antiferromagnet on a simple cubic lattice. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm which is based on Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical value. The dynamic critical exponent was estimated to be z=(1.43\pm 0.03), which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Comparisons are made of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF_3 are presented.Spin-dynamics simulations have been used to investigate the dynamic behavior of RbMnF_3, treating it as a classical Heisenberg antiferromagnet on a simple cubic lattice. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm which is based on Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical value. The dynamic critical exponent was estimated to be z=(1.43\pm 0.03), which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Comparisons are made of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF_3 are presented.

arXiv:cond-mat/9912374Dec 20, 19990 citations

Critical dynamics of the spin–boson model

Mikhail Gennag'evich Vasin, S. V. Remizov, Andrey A. Elistratov

arXiv:2501.12457Physica A Statistical Mechanics and its ApplicationsJul 22, 20260 citations

Critical dynamics of the simple-cubic Heisenberg antiferromagnet RbMnF3: Extrapolation to q=0

Shan-Ho Tsai, David Paul Landau

Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of ${\mathrm{RbMnF}}_{3},$ treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent z between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\ifmmode\pm\else\textpm\fi{}0.03,$ in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at ${T}_{c},$ seen in experiments and previous simulations, but absent in the renormalization-group and mode-coupling theories, is shown to be solely in the longitudinal component.Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of ${\mathrm{RbMnF}}_{3},$ treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent z between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\ifmmode\pm\else\textpm\fi{}0.03,$ in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at ${T}_{c},$ seen in experiments and previous simulations, but absent in the renormalization-group and mode-coupling theories, is shown to be solely in the longitudinal component.

arXiv:cond-mat/0301526Physical review. B, Condensed matterMar 17, 200323 citations

Critical dynamics in a soluble model of dilute ferromagnetism

H. G. E. Hentschel

The European Physical Journal BDec 1, 19800 citations

Spin-dynamics simulations of the magnetic dynamics of RbMnF3 and direct comparison with experiment

Shan-Ho Tsai, Alex Bunker, David Paul Landau

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L<~60.$ This system is widely recognized as an appropriate model for the magnetic properties of ${\mathrm{RbMnF}}_{3}.$ Time evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using an algorithm implemented by Krech et al., which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\ifmmode\pm\else\textpm\fi{}0.03),$ which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the line shapes obtained from our simulations with very recent experimental results for ${\mathrm{RbMnF}}_{3}$ are presented.Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L<~60.$ This system is widely recognized as an appropriate model for the magnetic properties of ${\mathrm{RbMnF}}_{3}.$ Time evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using an algorithm implemented by Krech et al., which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\ifmmode\pm\else\textpm\fi{}0.03),$ which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the line shapes obtained from our simulations with very recent experimental results for ${\mathrm{RbMnF}}_{3}$ are presented.

arXiv:cond-mat/9910429Physical review. B, Condensed matterJan 1, 200028 citations

Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of

{\mathrm{RbMnF}}_{3},

treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent z between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\ifmmode\pm\else\textpm\fi{}0.03,$ in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at

{T}_{c},

seen in experiments and previous simulations, but absent in the renormalization-group and mode-coupling theories, is shown to be solely in the longitudinal component.

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes

L<~60.

This system is widely recognized as an appropriate model for the magnetic properties of

{\mathrm{RbMnF}}_{3}.

Time evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using an algorithm implemented by Krech et al., which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\ifmmode\pm\else\textpm\fi{}0.03),$ which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the line shapes obtained from our simulations with very recent experimental results for

{\mathrm{RbMnF}}_{3}

are presented.