# RPA Green's Functions of the Anisotropic Heisenberg Model

## TL;DR

This paper presents a pedagogic solution to the anisotropic Heisenberg model using RPA, calculating Green's functions and correlations for complex interactions, accessible to graduate students and physicists.

## Contribution

It provides a comprehensive, accessible RPA-based method for solving the anisotropic Heisenberg model with complex interactions, including next-nearest neighbors.

## Key findings

- Calculated Green's functions and pair correlations for the model.
- Demonstrated the method's pedagogic clarity and accessibility.
- Extended the solution to include complex interaction terms.

## Abstract

We solve in random-phase approximation the anisotropic Heisenberg model, including nearest and next-nearest neighbour interactions by calculating all Green's functions and pair correlation functions in a cumulant decoupling scheme. The general exposition is pedagogic in tone and is intended to be accessible to any graduate student or physicist who is not an expert in the field.