Soviet Journal of Low Temperature Physics

Relaxation of the energy density in a linear Ising system at low temperatures

Gersh O. Berim, Камалов Равиль Гатуфович

Published Dec 1, 1985• 0 citations

Abstract

Using a microscopic approach we have studied the relaxation of homogenous fluctuations in the energy density in Ising spin chains with S = 1/2 and S = 1. It is shown that the nature of the relaxation as T→0 depends significantly on the spin magnitude and on the spin–lattice interaction.

DOI: 10.1063/10.0031404

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Soviet Journal of Low Temperature Physics

Relaxation of the energy density in a linear Ising system at low temperatures

Gersh O. Berim, Камалов Равиль Гатуфович

Published Dec 1, 1985• 0 citations

Publisher

Abstract

DOI: 10.1063/10.0031404

Related papers

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arXiv:1606.03985Physical review. B./Physical review. BOct 11, 201624 citations

{}_{2}

{}_{6}

. It has recently become clear that there was a surprising discrepancy between the observations: the energy gap in the quantum disordered regime as measured by nuclear magnetic resonance was approximately twice that measured by other methods. Here, the authors show via careful analysis of the low-temperature excitations that this is not a discrepancy, rather, it is in fact to be expected from the subtle interactions between the excitations. Although the underlying spin excitations are bosonic, their interactions transmute them into fermions, and this is a key ingredient in understanding the experiments.

The energy relaxation in the two-dimensional Ising model, with temperature greater than

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

and in a spin system having a 5120\ifmmode\times\else\texttimes\fi{}5120 lattice, is studied using supercomputer-conducted Monte Carlo simulation. The critical exponents of the linear and nonlinear relaxation times of the internal energy are respectively estimated to be ${\mathrm{\ensuremath{\Delta}}}_{\mathit{E}}^{(\mathit{l})}$=2.064\ifmmode\pm\else\textpm\fi{}0.026 and ${\mathrm{\ensuremath{\Delta}}}_{\mathit{E}}^{(\mathrm{nl})}$=1.132\ifmmode\pm\else\textpm\fi{}0.080, being consistent with the Racz scaling law ${\mathrm{\ensuremath{\Delta}}}_{\mathit{E}}^{(\mathit{l})}$-${\mathrm{\ensuremath{\Delta}}}_{\mathit{E}}^{(\mathrm{nl})}$=1-\ensuremath{\alpha}, where \ensuremath{\alpha} is the critical exponent of the specific heat. Based on the author's previous result in which the critical exponent of the linear relaxation for magnetization was determined as ${\mathrm{\ensuremath{\Delta}}}_{\mathit{M}}^{(\mathit{l})}$=2.076\ifmmode\pm\else\textpm\fi{}0.005, it is strongly suggested that ${\mathrm{\ensuremath{\Delta}}}_{\mathit{E}}^{(\mathit{l})}$=${\mathrm{\ensuremath{\Delta}}}_{\mathit{M}}^{(\mathit{l})}$.

1/{T}_{1}

in spin-

\frac{1}{2}

chain systems. This quantity is directly related to local, dynamical spin-spin correlation functions. The results agree in the low-temperature regime with bosonization predictions, and show interesting deviations from this behavior at intermediate temperatures.