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Field Theory Simulations on a Fuzzy Sphere - an Alternative to the Lattice

Julieta Medina·Wolfgang Bietenholz·Frank Hofheinz·Denjoe O'Connor
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Abstract

We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d λϕ^4 model. The regularisation consists of a fuzzy sphere with radius R for the two spatial directions, plus a discrete Euclidean time. The fuzzy sphere approximates the algebra of functions of the sphere with a matrix algebra, and the scalar field is represented by a Hermitian N x N matrix at each time site. We evaluate the phase diagram, where we find a disordered phase and an ordered regime, which splits into phases of uniform and non-uniform order. We discuss the behaviour of the model in different limits of large N and R, which lead to a commutative or to a non-commutative λϕ^4 model in flat space.

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Julieta Medina, Wolfgang Bietenholz, Frank Hofheinz, Denjoe O'Connor. 2005-09-28. Field Theory Simulations on a Fuzzy Sphere - an Alternative to the Lattice. https://arxiv.org/abs/hep-lat/0509162

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