On the type of the temperature phase transition in O(N) models within a perturbative analysis

TL;DR

This paper analyzes the nature of temperature-induced phase transitions in O(N) scalar field models using a beyond-super-daisy approximation, revealing how the transition type varies with coupling strength and N.

Contribution

It provides a perturbative analysis showing the dependence of phase transition order on coupling and N, including the role of specific diagrams like the sunset diagram.

Findings

Transition changes from weak first-order to second-order with increasing coupling.

The transition type depends on the value of the coupling constant.

Results agree with recent Monte Carlo simulations for the O(1) model.

Abstract

We investigate the type of the temperature phase transition in the $N$ component $\la \phi^4$ ($O(N)$) model of scalar fields. Actual calculations are carried out in the beyond-super-daisy approximation (BSDA). The cases $N = 1$ and larger $N$ are considered separately. Using the solutions of gap equations we show that the character of the phase transition depends on the account for graphs BSDA. The role of different kinds of diagrams (especially the "sunset" one) is clarified. It is shown in a perturbation theory in the effective expansion parameter $N^{- 1/3}$ that the kind of the phase transition depends on the value of coupling $\la$. It turns from a weak first-order to the second-order one for increasing $\la$. This is in agreement with the observation found recently for the $O(1)$ model in Monte Carlo simulations on a lattice. Comparison with results of other authors is given.