Wilson RG of Noncommutative $\Phi_{4}^4$

TL;DR

This paper investigates phi-four theory on noncommutative spaces using renormalization group techniques and matrix models, identifying three fixed points that correspond to different phase transitions.

Contribution

It introduces a combined approach of Wilson RG and matrix models to analyze phase transitions in noncommutative phi-four theory, revealing three distinct fixed points.

Findings

Identification of three fixed points: disordered-to-non-uniform-ordered, disordered-to-uniform-ordered, and non-uniform to uniform order transitions.

Connection of fixed points to specific values of the noncommutativity parameter .

Insights into phase structure of noncommutative ^4 theory.

Abstract

We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large $N$. Three fixed points are identified. The matrix model $\theta=\infty$ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at $\theta=0$ which describes the disordered-to-uniform-ordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of $\theta$ which is associated with the transition between non-uniform-order and uniform-order phases.