Optimal Linear Glauber Model

Sahoo, Shaon and Ganguly, Soumya Kanti (2015) Optimal Linear Glauber Model. In: JOURNAL OF STATISTICAL PHYSICS, 159 (2). pp. 336-357.

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Abstract

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Item Type:	Journal Article
Publication:	JOURNAL OF STATISTICAL PHYSICS
Publisher:	SPRINGER
Additional Information:	Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords:	KINETIC ISING-MODEL; STATISTICS; DYNAMICS; CHAIN
Department/Centre:	Division of Chemical Sciences > Solid State & Structural Chemistry Unit Division of Physical & Mathematical Sciences > Physics
Date Deposited:	28 Apr 2015 07:41
Last Modified:	28 Apr 2015 07:41
URI:	http://eprints.iisc.ac.in/id/eprint/51428

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