The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model

Abstract

We present a non-perturbative study of the lambda phi**4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large lambda it contains a "striped phase", which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed non-commutativity parameter. To this end, we introduce a dimensional lattice spacing based on the decay of the correlation function. Our results provide evidence for the existence of a striped phase even in the DSL, which implies the spontaneous breaking of translation symmetry. Due to the non-locality of this model, this does not contradict the Mermin-Wagner Theorem.

21 pages, LaTex, 9 figures, 1 table, extended version published in JHEP

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Cited by in corpus (14)

• Lectures on Matrix Field Theory I
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• Asymmetric hermitian matrix models and fuzzy field theory
• Second moment fuzzy-field-theory-like matrix models
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Emergent geometry from random multitrace matrix models
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• A Multitrace Approach to Noncommutative Φ_2^4
• Renormalization on the fuzzy sphere
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature