Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model

Abstract

We regularise the 3d λϕ^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent rôle. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and λ. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.

31 pages, 15 figures

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Cited by in corpus (18)

• Lectures on Matrix Field Theory I
• New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• Uniform order phase and phase diagram of scalar field theory on fuzzy $\mathbb{C}{P}^n$
• 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
• A Multitrace Approach to Noncommutative Φ_2^4
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4
• Phase structure of fuzzy black holes
• Fuzzy Scalar Field Theory as Matrix Quantum Mechanics
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Wilson RG of Noncommutative ${\Phi }_4^4$