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

Details Probing the fuzzy sphere regularisation in simulations of the 3d λ φ^4 model Probing the fuzzy sphere regularisation in simulations of the 3d λ φ^4 model

2007-12-20

arxiv.org/abs/0712.3366v1

JHEP 0804:041,2008

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 15 figures

Scientific paper

10.1088/1126-6708/2008/04/041

We regularise the 3d \lambda \phi^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 r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. 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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