The continuum limit of the non-commutative lambda phi^4 model

TL;DR

This paper numerically investigates a 3D non-commutative bbb4 model, revealing phase structures, a stable dispersion relation in the continuum limit, and persistent UV/IR mixing effects.

Contribution

It provides the first detailed phase diagram and continuum analysis of the non-commutative bbb4 model, demonstrating the persistence of the striped phase and UV/IR mixing non-perturbatively.

Findings

Identification of ordered and striped phases.

Establishment of a non-perturbative continuum limit.

Observation of UV/IR mixing effects.

Abstract

We present a numerical study of the \lambda \phi^{4} model in three Euclidean dimensions, where the two spatial coordinates are non-commutative (NC). We first show the explicit phase diagram of this model on a lattice. The ordered regime splits into a phase of uniform order and a ``striped phase''. Then we discuss the dispersion relation, which allows us to introduce a dimensionful lattice spacing. Thus we can study a double scaling limit to zero lattice spacing and infinite volume, which keeps the non-commutativity parameter constant. The dispersion relation in the disordered phase stabilizes in this limit, which represents a non-perturbative renormalization. From its shape we infer that the striped phase persists in the continuum, and we observe UV/IR mixing as a non-perturbative effect.