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arXiv · 1403.3318

The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model

Héctor Mejía-Díaz·Wolfgang Bietenholz·Marco Panero
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Abstract

We present a non-perturbative study of the lambda phi**4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large lambda it contains a "striped phase", which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed non-commutativity parameter. To this end, we introduce a dimensional lattice spacing based on the decay of the correlation function. Our results provide evidence for the existence of a striped phase even in the DSL, which implies the spontaneous breaking of translation symmetry. Due to the non-locality of this model, this does not contradict the Mermin-Wagner Theorem.

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Héctor Mejía-Díaz, Wolfgang Bietenholz, Marco Panero. 2014-10-14. The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model. https://doi.org/10.1007/jhep10(2014)056

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