Phase diagram and dispersion relation of the non-commutative λ φ^{4} model in d=3

Details Phase diagram and dispersion relation of the non-commutative λ φ^{4} model in d=3 Phase diagram and dispersion relation of the non-commutative λ φ^{4} model in d=3

2004-04-02

arxiv.org/abs/hep-th/0404020v2

JHEP0406:042,2004

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, 24 figures, final version published in JHEP

Scientific paper

10.1088/1126-6708/2004/06/042

We present a non-perturbative study of the \lambda \phi^{4} model in a three dimensional Euclidean space, where the two spatial coordinates are non-commutative. Our results are obtained from numerical simulations of the lattice model, after its mapping onto a dimensionally reduced, twisted Hermitian matrix model. In this way we first reveal the explicit phase diagram of the non-commutative \lambda \phi^{4} lattice model. We observe that the ordered regime splits into a phase of uniform order and a phase of two stripes of opposite sign, and more complicated patterns. Next we discuss the behavior of the spatial and temporal correlators. From the latter we extract the dispersion relation, which allows us to introduce a dimensionful lattice spacing. To extrapolate to zero lattice spacing and infinite volume we perform a double scaling limit, which keeps the non-commutativity tensor constant. The dispersion relation in the disordered phase stabilizes in this limit, which represents a non-perturbative renormalization. In particular this confirms the existence of a striped phase in the continuum limit, in accordance with a conjecture by Gubser and Sondhi. The extrapolated dispersion relation also exhibits UV/IR mixing as a non-perturbative effect. Finally we add some observations about a Nambu-Goldstone mode in the striped phase, and about the corresponding model in d=2.

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