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Physical review. B, Condensed matter

Dynamic finite-size effect in an infinite-range classical antiferromagnetic spin model

Suhk Kun Oh, Chang No Yoon, Jean Soo Chung

Published Jan 1, 1997• 0 citations
Publisher

Abstract

As a further test of the dynamic scaling method proposed by us previously, dynamic finite-size effect in an infinite-range classical antiferromagnetic spin model, which is an anisotropic version of two-sublattice Lieb-Mattis model, is studied. Application of our dynamic scaling method to the model yields time scaling exponents similar to those of the infinite-range ferromagnetic classical spin van der Waals model. With the hereby obtained time scaling variables, we can successfully collapse the time-dependent correlation functions of the model into universal curves.

DOI
10.1103/physrevb.55.44

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As a further test of the dynamic scaling method proposed by us previously, dynamic finite-size effect in an infinite-range classical antiferromagnetic spin model, which is an anisotropic version of two-sublattice Lieb-Mattis model, is studied. Application of our dynamic scaling method to the model yields time scaling exponents similar to those of the infinite-range ferromagnetic classical spin van der Waals model. With the hereby obtained time scaling variables, we can successfully collapse the time-dependent correlation functions of the model into universal curves.
Explicit dynamic finite-size scaling in the time-dependent correlation functions for the three-dimensional classical XY\mathrm{XY}XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time-scaling variables of the model. Time-dependent correlation functions of the model for different numbers of spins could be collapsed into universal curves. Compared to infinite-range spin models, the width of the scaling region is found to be much narrower.
A phenomenological dynamic scaling method is proposed and utilized to interpret finite-size effects in the time-dependent correlation function for the classical spin van der Waals model. We claim that the equations of motion for the classical spin van der Waals model are well defined only within a certain characteristic time. The order of magnitude for the size-dependent maximum time interval of the time-dependent correlation function, analytically obtained in the large N limit via the method of Laplace by Dekeyser and Lee, is found to be related to our characteristic time. As a by-product of this work, time scaling variables are found with which we can completely collapse the time-dependent correlation functions of the classical spin van der Waals model into one curve. \textcopyright{} 1996 The American Physical Society.
Explicit dynamic finite-size scaling in the time-dependent correlation functions for the two-dimensional classical XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time scaling variables of the model. It shows nontrivial dynamic finite-size scaling behavior near and below TKT for the total spin correlation function. Since the model is critical for all temperatures below TKT, the time scaling exponent is markedly different from that of the three-dimensional classical XY model at short times. There also appears to be another dynamic scaling region with a different time scaling exponent at T⩽TKT for a fairly wide intermediate time interval.
Abstract We consider an infinite-range Ising model under the Glauber dynamics and determine the finite-size effect on the distribution of two spin variables as a perturbation of O 1 / N . Based on several considerations, ordinary differential equations are derived for describing the time development of both a two-body correlation and the autocorrelation function of magnetization. The results of the calculation fit the simulation results, unless the perturbation theory breaks down because of critical phenomena or magnetization reversal.
Spin dynamics simulations have been used to study dynamic critical behavior of classical Heisenberg magnets. The temporal evolutions of the spin configurations were determined numerically from coupled equations of motion by a fourth-order predictor corrector method, with initial spin configurations generated by Monte-Carlo simulations. The neutron scattering function, S (q, ω), was calculated from the space and time displaced spin-spin correlation function and the dynamic critical exponent z was extracted using dynamic finite size scaling theory. For both ferromagnetic and antiferromagnetic models we find good agreement with theoretical predictions and experimental results.