A Multitrace Approach to Noncommutative Φ_2^4

Abstract

In this article we provide a multitrace analysis of the theory of noncommutative ${\Phi }^4$ in two dimensions on the fuzzy sphere ${\mathbf{S}}_{N,\Omega }^2$, and on the Moyal-Weyl plane ${\mathbf{R}}_{\theta ,\Omega }^2$, with a non-zero harmonic oscillator term added. The doubletrace matrix model symmetric under $M⟶-M$ is solved in closed form. An analytical prediction for the disordered-to-non-uniform-ordered phase transition and an estimation of the triple point, from the termination point of the critical boundary, are derived and compared with previous Monte Carlo measurement.

v1:21 pages. v2:30 pages, 4 figures (9 graphs) and references added. In this version we have added two full-blown sections on Monte Carlo results and the non-perturbative multitrace effective potential which strengthen our original findings and give more substance to the paper

References in corpus (8)

• Finite temperature phase transition of a single scalar field on a fuzzy sphere
• The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CP^n
• New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• Uniform order phase and phase diagram of scalar field theory on fuzzy $\mathbb{C}{P}^n$
• Random matrix approach to scalar fields on fuzzy spaces
• Emergent geometry from random multitrace matrix models
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4

Cited by in corpus (4)

• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• Emergent geometry from random multitrace matrix models
• Quantum Gravity as a Multitrace Matrix Model
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space