Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

Abstract

We construct and analyze the phase diagram of a self-interacting matrix field in two dimensions coupled to the curvature of the non-commutative truncated Heisenberg space. In the infinite size limit, the model reduces to the renormalizable Grosse-Wulkenhaar's. The curvature term proves crucial for the diagram's structure: when turned off, the triple point collapses into the origin as matrices grow larger; when turned on, the triple point recedes from the origin proportionally to the coupling strength and the matrix size. The coupling attenuation that turns the Grosse-Wulkenhaar model into a renormalizable version of the ${\varphi }_{\star }^4$-model cannot stop the triple point recession. As a result, the stripe phase escapes to infinity, removing the problems with UV/IR mixing.

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Cited by in corpus (4)

• Approximate treatment of noncommutative curvature in quartic matrix model
• 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