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arXiv · 0712.3366

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

Julieta Medina·Wolfgang Bietenholz·Denjoe O'Connor
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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.

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Julieta Medina, Wolfgang Bietenholz, Denjoe O'Connor. 2007-12-20. Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model. https://doi.org/10.1088/1126-6708%2F2008%2F04%2F041

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