A 2 Loop 2PPI Analysis of $\lambda\phi^4$ at Finite Temperature

TL;DR

This paper computes the finite temperature effective potential of the b5c4b5c4c6b1^4 theory using a two-loop 2PPI expansion, revealing a change from a first-order to a second-order phase transition at two loops.

Contribution

It introduces a two-loop 2PPI expansion calculation for b5c4b5c4c6b1^4 at finite temperature, showing the phase transition nature changes at this order.

Findings

One-loop 2PPI predicts a first-order phase transition.

Two-loop 2PPI predicts a second-order phase transition.

Critical exponents are mean field.

Abstract

We calculate the finite temperature effective potential of $\lambda\phi^4$ at the two loop order of the 2PPI expansion. This expansion contains all diagrams which remain connected when two lines meeting at the same point are cut and therefore sums systematically the bubble graphs. At one loop in the 2PPI expansion, the symmetry restoring phase transition is first order. At two loops, we find a second order phase transition with mean field critical exponents.