Triple Point of a Scalar Field Theory on a Fuzzy Sphere

Abstract

The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These three phases are expected to meet at a triple point. By studying the infinite matrix size limit, we locate the position of this triple point to within a small triangle in terms of the parameters of the model. We find the triple point is closer to the coordinate origin of the phase diagram than previous estimates but broadly consistent with recent analytic predictions.

arXiv comment12 pages, 5 figures

References in corpus (27)

• String Theory and Noncommutative Geometry
• The quantum structure of spacetime at the Planck scale and quantum fields
• 2D Gravity and Random Matrices
• The Non-Commutative Geometry of the Quantum Hall Effect
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Topologically nontrivial field configurations in noncommutative geometry
• On Finite 4D Quantum Field Theory in Non-Commutative Geometry
• Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
• Scaling Limits of the Fuzzy Sphere at one Loop
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum ϕ^4_2
• 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
• Monte Carlo determination of the critical coupling in ${\varphi }_2^4$ theory
• Effective action and phase transitions of scalar field on the fuzzy sphere
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
• Asymmetric hermitian matrix models and fuzzy field theory
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Time dependence of entanglement entropy on the fuzzy sphere
• A Multitrace Matrix Model from Fuzzy Scalar Field Theory
• 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

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• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Eigenvalue-flipping Algorithm for Matrix Monte Carlo
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature