# Reference approach in theory of pseudospin systems

## TL;DR

This paper develops a theoretical framework using cluster approximation methods to analyze quantum pseudospin systems with complex interactions, providing new formulas and insights into their thermodynamic and excitation properties.

## Contribution

It introduces a consistent cluster expansion approach for quantum pseudospin systems and derives explicit expressions for Green functions within this framework.

## Key findings

- Derived an Ornstein-Zernike type equation for reference Green functions.
- Obtained explicit pair cumulant Green function in two-particle approximation.
- Analyzed thermodynamic properties and excitation spectra of the transverse field Ising model.

## Abstract

For theoretical description of pseudospin systems with essential short-range and long-range interactions we use the method based on calculations of the free energy functional with taking into account the short-range interactions within the reference approach in cluster approximation. We propose a consistent formulation of the cluster expansion method for quantum pseudospin systems. We develop a method allowing one to obtain within the cluster approximation an Ornstein-Zernike type equation for reference cumulant Green function of an arbitrary order. In the two-particle cluster approximation we derived an explicit expression for pair temperature cumulant Green function of the reference system. In the cluster random phase approximation we calculated and studied thermodynamic characteristics, elementary excitation spectrum, and integral intensities of the Ising model in transverse field.