Random 3D Spin System Under the External Field and Dielectric Permittivity Superlattice Formation

TL;DR

This paper models a 3D disordered spin system as a dielectric medium, developing a microscopic statistical approach to analyze its properties and generalize the Clausius-Mossotti formula for dielectric permittivity.

Contribution

It introduces a novel microscopic framework reducing a 3D spin problem to two 1D problems and derives a generalized dielectric permittivity equation.

Findings

Calculated the polarizability coefficient considering collective effects

Generalized Clausius-Mossotti formula for dielectric constant

Derived a new equation for dielectric permittivity incorporating the generalized formula

Abstract

A dielectric medium consisting of roughly polarized molecules is treated as a 3D disordered spin system (spin glass). A microscopic approach for the study of statistical properties of this system on micrometer space scale and nanosecond time scale of standing electromagnetic wave is developed. Using ergodic hypothesis the initial 3D spin problem is reduced to two separate 1D problems along external field propagation. The first problem describes the disordered spin chain system while the second one describes a disordered N-particle quantum system with relaxation in the framework of Langevin-Schroedinger (L-Sch) type equation. Statistical properties of both systems are investigated in detail. Basing on these constructions, the coefficient of polarizability, related to collective orientational effects, is calculated. Clausius-Mossotti formula for dielectric constant is generalized. For dielectric permittivity function generalized equation is found taking into account Clausius-Mossotti generalized formula.