Cluster Expansion Approach to the Effective Potential in $\Phi^4_{2+1}$-Theory

TL;DR

This paper uses a truncated dynamical equations approach to study spontaneous symmetry breaking in 2+1 dimensional Phi^4 theory, revealing a second order phase transition influenced by higher-order Green functions.

Contribution

It introduces a method applying truncated equations of motion for Green functions up to the 4-point level to analyze phase transitions in Phi^4_{2+1} theory, highlighting the impact of including higher-order correlations.

Findings

Second order phase transition observed with 3-point function inclusion

4-point function significantly alters the effective potential shape

Critical coupling is affected by higher-order Green functions

Abstract

We apply a truncated set of dynamical equations of motion for connected equal-time Green functions up to the 4-point level to the investigation of spontaneous ground state symmetry breaking in $\Phi^4_{2+1}$ quantum field theory. Within our momentum space discretization we obtain a second order phase transition as soon as the connected 3-point function is included. However, an additional inclusion of the connected 4-point function still shows a significant influence on the shape of the effective potential and the critical coupling.