The antiferromagnetic phi4 Model, I. The Mean-field Solution

TL;DR

This paper explores the complex phase structure of the four-dimensional phi4 scalar model using mean-field approximation, revealing various magnetic phases, phase transitions, and particle phenomena, with implications for lattice regularization.

Contribution

It provides a detailed mean-field analysis of the phi4 model's phase diagram, including magnetic phases and particle behavior, highlighting new features like inhomogeneous vacua and chiral bosons.

Findings

Identification of para-, ferro-, ferri-, and antiferromagnetic phases

Discovery of commensurate-incommensurate transitions

Observation of multiple particles described by the same quantum field

Abstract

Certain higher dimensional operators of the lagrangian may render the vacuum inhomogeneous. A rather rich phase structure of the phi4 scalar model in four dimensions is presented by means of the mean-field approximation. One finds para- ferro- ferri- and antiferromagnetic phases and commensurate-incommensurate transitions. There are several particles described by the same quantum field in a manner similar to the species doubling of the lattice fermions. It is pointed out that chiral bosons can be introduced in the lattice regularized theory.