One-Dimensional Time-Dependent Frustrated and Disordered Ising Model

Abstract

We study the combined effects of disorder and frustration on time dependences of thermodynamical quantities. We consider the kinetic Ising model in the version proposed by Glauber [1]. This model has already been considered at different levels of complexity. Admission of a possibility of the exchange integrals taking random values complicates the problem, although it does not introduce competition, but it can still be analytically investigated ([2] and [3]). Additional complexity appears when frustration is admitted. The simplest model with frustration is the one-dimensional antiferromagnetic Ising model in a magnetic field. However, in this model only for zero magnetic field it is possible to derive expressions for the time dependences of thermodynamic quantities, as only then the time derivative of the n-spin correlation function can be expressed in terms of the corresponding n-spin correlation functions. For other models the equation of motion of the n-spin correlation function includes also other correlations, which means that all 2 correlation functions must be taken into regard to derive an expression for anyone of them. In literature this rule is known as the BBGKY hierarchy [4]. In certain particular cases the disordered one-dimensional Ising model has been analysed in an external magnetic field. The case when the magnetic field H can be assumed to tend to zero has been studied by Jose et al. [5]. A radically different situation of the random fields of infinite values when the system