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Journal of Physics C Solid State Physics

The phase transition of spin glasses in an external AC field

Takayuki Shirakura, Hajime Takayama

Published Jul 20, 1986• 1 citation
Publisher

Abstract

By means of the soft spin version of the SK spin glass the phase transition in an external AC field is investigated. It is shown that a well defined phase transition temperature Tc exists and depends on the amplitude hAC and frequency nu of the AC field. The dynamical AC non-linear susceptibility chi 2(3 nu ) exhibits a peak at Tc whose height and width are proportional to nu -1/2 and nu 1/2 respectively.

DOI
10.1088/0022-3719/19/20/008

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By means of the soft spin version of the SK spin glass the phase transition in an external AC field is investigated. It is shown that a well defined phase transition temperature Tc exists and depends on the amplitude hAC and frequency nu of the AC field. The dynamical AC non-linear susceptibility chi 2(3 nu ) exhibits a peak at Tc whose height and width are proportional to nu -1/2 and nu 1/2 respectively.
The dynamical mean field theory of spin glasses is investigated in systems with non-zero mean of the infinitely-ranged random exchange interactions under uniform but alternating external magnetic fields. A perturbational expansion with respect to the interaction uσi4 introduced in a soft-spin version of the model is analyzed by means of the diagrammatic method. Restricting ourselves to its lowest order (single-loop) approximation, we examine relaxational dynamics of the model spin glass and clarify nature of its phase transition in the presence of an ac external field. The results provide a new clue to ac nonlinear measurements on spin glasses.
We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three-dimensional cubic lattice. We measure the ac susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law $\ensuremath{\tau}\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}z\ensuremath{\nu}}$ with Tc=0.19(4){T}_{c}=0.19(4)Tc​=0.19(4) and $z\ensuremath{\nu}=5.0(5)$. Although our data indicate that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.
By means of two different methods in a Monte Carlo simulation, the authors calculate the AC susceptibilities chi ( omega ) and relaxation time distributions g( tau ) in the +or-J Ising two-dimensional (2D) and three-dimensional (3D) spin glasses. The data obtained by the two methods separately are confirmed to be consistent with each other through the fluctuation dissipation theorem chi ( omega )=(1/T) integral d tau g( tau )/(1-i omega tau ). The imaginary parts Im chi of the AC susceptibilities show a characteristic difference in the 2D and 3D spin glasses; as the frequency of the AC field is decreased, the height of the peak of Im chi becomes higher in the 2D spin glass, and lower in the 3D spin glass. They can also see a difference between the g( tau ) distributions in the 2D and 3D spin glasses, reflected by the difference in the chi ( omega )-values. In the 3D spin glass, Im chi has no frequency dependence at low temperatures, suggesting that the fluctuation spectrum of the magnetization shows 1/f-noise behaviour in the spin-glass phase.
The author has first solved numerically the mean field equations of the SK model obtained with Parisi's ansatz (1980) for a wide range of values of the temperature and the magnetic field. Then, using Sompolinsky and Zippelius' formulation of the spin-glass dynamics (1982) that shows that the finite time spin correlations decay algebraically with a power nu (T, h), the author obtains the exact behaviour nu (T, h=0) down to T/T c =0.07 and the much weaker dependence on the magnetic field for several values of the temperature.