A Few Exact Solutions for the Model of Equal Spin-Spin Interactions

Abstract

For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact relations for the means to describe the thermodynamics of the model under consideration.

Thermodynamics of the model of equal spin-spin interactions

“…To find the correlation functions R k,1 , we must obtain one more system of equations. We use the equation derived in [1] based on an exact solution of the equation of motion for the operator S z f :…”

“…A simplified model for describing the properties of spin systems in mesoscopic magnetically active clusters was proposed in [1]. The clusters can be used as the working media in realizing quantum computing algorithms [2], [3], a branch of physics that has been vigorously developing during the last decade.…”

“…The isotropic version of the model (A = B) was investigated in [4], where the nonergodicity of its dynamics was revealed. Here, we continue the study of the ESSI model begun in [1] and consider the thermodynamic behavior of spins with equal interactions between them. The analysis of the thermodynamics of any multiparticle system is an inalienable part of a full-fledged analysis of a model aspiring to a description of physical properties of real systems.…”

The NMR line shape of a system of nuclear spins with equal spin-spin coupling constants

“…The model defined by Hamiltonian (2) is called the ESSI model [6]. Passing to Hamiltonian (2) significantly simplifies analyzing the thermodynamic [7] and magnetic [8] properties of finite spin systems.…”

“…A simplified model for describing the properties of spin systems in mesoscopic magnetoactive clusters was proposed in [6]. This model was called the equal spin-spin coupling model (ESSI), and it can be studied by exact analytic methods.…”