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

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 $Φ^4_{2+1}$ 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.

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