Journal of the Korean Physical Society

Exact time evolution of the total spin components and its application to the classical spin van der Waals model in transverse magnetic fields

Suhk Kun Oh

Published Sep 1, 2012• 0 citations

Abstract

The exact time evolution expressions for the total spin components are obtained by solving the equations of motion for the classical spin van der Waals model in transverse magnetic fields. They are given in terms of Jacobi elliptic functions and are examined in detail. They are also used to obtain the time-dependent total spin correlation functions by adopting equilibrium configurations acquired via a heat bath algorithm. The time-dependent total spin correlation functions are interpreted by utilizing the motion of the tip of the total spin vector on the surface of a Bloch sphere.

DOI: 10.3938/jkps.61.679

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Journal of the Korean Physical Society

Exact time evolution of the total spin components and its application to the classical spin van der Waals model in transverse magnetic fields

Suhk Kun Oh

Published Sep 1, 2012• 0 citations

Publisher

Abstract

DOI: 10.3938/jkps.61.679

Related papers

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Y. K. Lee, I. M. Kim

Canadian Journal of PhysicsJan 1, 19901 citation

The time-dependent autocorrelation function has been derived for the

x

component of the total spin for the

S=\frac{1}{2}

constant-coupling anisotropic Heisenberg model, i.e., the Van der Waals system. For

T>{T}_{c}

, the time correlation is shown to be Gaussian for both

\mathrm{XY}

-like and Ising-like regimes of the model. For

T<{T}_{c}

, the correlation function is still Gaussian if the model is

\mathrm{XY}

-like; but it is oscillatory if the model is Ising-like. Critical slow down appears only with the Ising-like system for this time-correlation function.

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

). The exponent \ensuremath{\kappa}, where 〈

{\mathit{s}}^{\mathit{x}}

(t)

{\mathit{s}}^{\mathit{x}}

(0)〉\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\kappa}}}$, as t\ensuremath{\rightarrow}\ensuremath{\infty}, is found to depend discontinuously on the spin-spin interaction strength R=

{\mathit{J}}_{\mathit{z}}

/J: \ensuremath{\kappa}=2 if R=0, \ensuremath{\kappa}=3 if 0R\ensuremath{\le}2 (R\ensuremath{\ne}1), \ensuremath{\kappa}=\ensuremath{\infty} if R=1, and \ensuremath{\kappa}=\ensuremath{\infty} if R>2. Slow decay in this model is attributed to nondimensional effects, e.g., cooperativity. Physical and mathematical mechanisms of the slow decay are described.