Numerical results on the Non-commutative \lambda \phi^4 Model

TL;DR

This paper presents numerical analysis of the non-commutative ^4 model, revealing altered phase diagrams, correlation functions, and dispersion relations due to UV/IR mixing in three-dimensional space with two non-commutative coordinates.

Contribution

It provides the first numerical results demonstrating the effects of UV/IR mixing on phase structure and correlation functions in the non-commutative ^4 model.

Findings

Changed phase diagram observed.

Unusual behavior of correlation functions.

Deformation of dispersion relation detected.

Abstract

The UV/IR mixing in the \lambda \phi^4 model on a non-commutative (NC) space leads to new predictions in perturbation theory, including Hartree-Fock type approximations. Among them there is a changed phase diagram and an unusual behavior of the correlation functions. In particular this mixing leads to a deformation of the dispersion relation. We present numerical results for these effects in d=3 with two NC coordinates.