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

Medina, Julieta and Bietenholz, Wolfgang and O'Connor, Denjoe (2007) Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model. Journal of High Energy Physics, 2008 (04). 041-041. ISSN 1029-8479

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Official URL: http://doi.org/10.1088/1126-6708/2008/04/041

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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:23
Last Modified: 26 Jul 2018 14:17
URI: http://dair.dias.ie/id/eprint/214

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