Employing Monte Carlo simulations, the equilibrium dynamic critical behavior or L×L×L simple cubic classical Heisenberg models with periodic boundary conditions are determined. From the long-time exponential decay of the time-displaced correlation function of the magnetization the linear (equilibrium) relaxation time τ is also determined. It is found that at the critical point Tc, τ grows like τ≂Lz with z=1.94±0.06. In the paramagnetic region a power-law divergence τ≂(T/Tc−1)−Δ was found with Δ=zν=1.38±0.04, which implies a dynamical critical exponent z=1.96±0.07. Both values are consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving forces.Employing Monte Carlo simulations, the equilibrium dynamic critical behavior or L×L×L simple cubic classical Heisenberg models with periodic boundary conditions are determined. From the long-time exponential decay of the time-displaced correlation function of the magnetization the linear (equilibrium) relaxation time τ is also determined. It is found that at the critical point Tc, τ grows like τ≂Lz with z=1.94±0.06. In the paramagnetic region a power-law divergence τ≂(T/Tc−1)−Δ was found with Δ=zν=1.38±0.04, which implies a dynamical critical exponent z=1.96±0.07. Both values are consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving forces.

Journal of Applied PhysicsMay 1, 199033 citations

Critical behavior of the quantum spin- anisotropic Heisenberg model

J. Ricardo de Sousa

Physica A Statistical Mechanics and its ApplicationsOct 1, 19985 citations

Construction of the correlation functions of the Heisenberg ferromagnet in the ferromagnetic and paramagnetic regions

Yu. A. Tserkovnikov

Theoretical and Mathematical PhysicsAug 1, 19797 citations

Dynamical critical behavior of the three-dimensional Heisenberg model

Pawel Peczak, David Paul Landau

We have carried out extensive Monte Carlo simulations of the dynamic critical behavior of L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L simple-cubic classical Heisenberg models with periodic boundary conditions. The equilibrium relaxation time \ensuremath{\tau} is determined from the long-time exponential decay of the time-displaced correlation function of the magnetization. Using finite-size scaling and corrections to scaling we find that at the critical point ${\mathit{T}}_{\mathit{c}}$ =(0.6929${)}^{\mathrm{\ensuremath{-}}1}$, \ensuremath{\tau} grows like \ensuremath{\tau}\ensuremath{\simeq} ${\mathit{L}}^{\mathit{z}}$ with z=1.96(6). In the paramagnetic region we show that the relaxation time is represented by a universal scaling function \ensuremath{\tau}${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{z}}$ vs (T/ ${\mathit{T}}_{\mathit{c}}$ -1)${\mathit{L}}^{1/\ensuremath{\nu}}$ with z=1.96(6). This estimate is consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving dipolar interactions. We also describe how a simple over-relaxation algorithm of Creutz and of Brown and Woch can be incorporated into the Metropolis sampling method for the classical Heisenberg model, thereby significantly reducing the critical slowing down; the resultant correlation time varies as \ensuremath{\tau}\ensuremath{\sim}(T/ ${\mathit{T}}_{\mathit{c}}$ -1${)}^{\mathrm{\ensuremath{-}}0.77}$, which implies z\ensuremath{\simeq}1.10.We have carried out extensive Monte Carlo simulations of the dynamic critical behavior of L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L simple-cubic classical Heisenberg models with periodic boundary conditions. The equilibrium relaxation time \ensuremath{\tau} is determined from the long-time exponential decay of the time-displaced correlation function of the magnetization. Using finite-size scaling and corrections to scaling we find that at the critical point ${\mathit{T}}_{\mathit{c}}$=(0.6929${)}^{\mathrm{\ensuremath{-}}1}$, \ensuremath{\tau} grows like \ensuremath{\tau}\ensuremath{\simeq}${\mathit{L}}^{\mathit{z}}$ with z=1.96(6). In the paramagnetic region we show that the relaxation time is represented by a universal scaling function \ensuremath{\tau}${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{z}}$ vs (T/${\mathit{T}}_{\mathit{c}}$-1)${\mathit{L}}^{1/\ensuremath{\nu}}$ with z=1.96(6). This estimate is consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving dipolar interactions. We also describe how a simple over-relaxation algorithm of Creutz and of Brown and Woch can be incorporated into the Metropolis sampling method for the classical Heisenberg model, thereby significantly reducing the critical slowing down; the resultant correlation time varies as \ensuremath{\tau}\ensuremath{\sim}(T/${\mathit{T}}_{\mathit{c}}$-1${)}^{\mathrm{\ensuremath{-}}0.77}$, which implies z\ensuremath{\simeq}1.10.

Physical review. B, Condensed matterJun 1, 199345 citations

A new approach to critical behaviour in the heisenberg model?

Vinod Mubayi

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJun 1, 19701 citation

{\mathit{T}}_{\mathit{c}}

=(0.6929${)}^{\mathrm{\ensuremath{-}}1}$, \ensuremath{\tau} grows like \ensuremath{\tau}\ensuremath{\simeq}

{\mathit{L}}^{\mathit{z}}

with z=1.96(6). In the paramagnetic region we show that the relaxation time is represented by a universal scaling function \ensuremath{\tau}${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{z}}$ vs (T/

{\mathit{T}}_{\mathit{c}}

-1)${\mathit{L}}^{1/\ensuremath{\nu}}$ with z=1.96(6). This estimate is consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving dipolar interactions. We also describe how a simple over-relaxation algorithm of Creutz and of Brown and Woch can be incorporated into the Metropolis sampling method for the classical Heisenberg model, thereby significantly reducing the critical slowing down; the resultant correlation time varies as \ensuremath{\tau}\ensuremath{\sim}(T/

{\mathit{T}}_{\mathit{c}}

-1${)}^{\mathrm{\ensuremath{-}}0.77}$, which implies z\ensuremath{\simeq}1.10.