Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space

Abstract

In this contribution, we summarize our recent studies of the phase structure of the Grosse-Wulkenhaar model and its connection to renormalizability. Its action contains a special term that couples the field to the curvature of the noncommutative background space. We first analyze the numerically obtained phase diagram of the model and its three phases: the ordered, the disordered, and the noncommutative stripe phase. Afterward, we discuss the analytical derivation of the effective action and the ordered-to-stripe transition line, and how the obtained expression successfully explains the curvature-induced shift of the triple point compared to the model without curvature. This shift also causes the removal of the stripe phase and makes the model renormalizable.

COST Action CA18108: Workshop on theoretical aspects of quantum gravity, 1-3 September 2022, Belgrade

References in corpus (5)

• 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 $\mathbb{C}{P}^n$
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models