# Linked Cluster Expansions on non-trivial topologies

## TL;DR

This paper discusses the use of linked cluster expansions to analyze lattice field theories, highlighting their convergence properties and applications to finite temperature and volume, with a focus on high-order series for critical behavior analysis.

## Contribution

The paper extends linked cluster expansions to finite temperature and volume, and demonstrates how high-order series can reveal critical behavior in lattice field theories.

## Key findings

- Series converge for free energies, correlations, and susceptibilities
- High-order susceptibility series provide insights into critical phenomena
- Achieved 20th order expansion for detailed analysis

## Abstract

Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result into convergent series for free energies, correlation functions and susceptibilities. The expansions have been generalized to field theories at finite temperature and to a finite volume. Detailed information on critical behaviour can be extracted from the high order behaviour of the susceptibility series. We outline some of the steps by which the 20th order is achieved.