Detecting scaling in phase transitions on the truncated Heisenberg algebra

Abstract

We construct and analyze a phase diagram of a self-interacting matrix field coupled to curvature of the non-commutative truncated Heisenberg space. The model reduces to the renormalizable Grosse-Wulkenhaar model in an infinite matrix size limit and exhibits a purely non-commutative non-uniformly ordered phase. Particular attention is given to scaling of model's parameters. We additionally provide the infinite matrix size limit for the disordered to ordered phase transition line.

arXiv commentv2: Paper restructured. New data and additional section added. Some notation changed. Major revision. v3: Typos from convention change corrected. Three figures added, one removed. Minor text changes

References in corpus (41)

• String Theory and Noncommutative Geometry
• Critical Phenomena and Renormalization-Group Theory
• Noncommutative Perturbative Dynamics
• The Non-Commutative Geometry of the Quantum Hall Effect
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Renormalization Group Approach to Matrix Models
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Scaling Limits of the Fuzzy Sphere at one Loop
• Phase structure of non-commutative scalar field theories
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Fuzzy Scalar Field Theory as a Multitrace Matrix Model
• Simulation of a scalar field on a fuzzy sphere
• A matrix phase for the phi^4 scalar field on the fuzzy sphere
• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Intrinsic non-commutativity of closed string theory
• Geometry of the Grosse-Wulkenhaar Model
• Effective action and phase transitions of scalar field on the fuzzy sphere
• The Hobbyhorse of Magnetic Systems: The Ising Model
• Properties of Higher-Order Phase Transitions
• New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere
• Lectures on Matrix Field Theory I
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• 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 $\mathbb{C}{P}^n$
• On the Phase Structure of Commuting Matrix Models
• The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Asymmetric hermitian matrix models and fuzzy field theory
• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Time dependence of entanglement entropy on the fuzzy sphere
• Renormalization group approach to matrix models via noncommutative space
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Computational Physics: An Introduction to Monte Carlo Simulations of Matrix Field Theory
• From Quantum Optics to Non-Commutative Geometry : A Non-Commutative Version of the Hopf Bundle, Veronese Mapping and Spin Representation
• Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model
• Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model

Cited by in corpus (7)

• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Second moment fuzzy-field-theory-like matrix models
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Approximate treatment of noncommutative curvature in quartic matrix model
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature