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arXiv · 1811.11112

Simulation of Scalar Field Theories with Complex Actions

Michael C. Ogilvie·Leandro Medina
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Abstract

Many scalar field theory models with complex actions are invariant under the antilinear ($PT$) symmetry operation $L^{\ast}(-\chi)=L(\chi)$. Models in this class include the $i\phi^{3}$ model, the Bose gas at finite density and Polyakov loop spin models at finite density. This symmetry may be used to obtain a dual representation where weights in the functional integral are real but not necessarily positive. For a subclass of models satisfying a dual positive weight condition, the partition function is manifestly positive. The sign problem is eliminated; such models are easily simulated by a simple local algorithm in any number of dimensions. Simulations of models in this subclass show a rich set of behaviors. Propagators may exhibit damped oscillations, indicating a clear violation of spectral positivity. Pattern formation may also occur, with both stripe and bubble morphologies possible. The existence of a positive representation is constrained by Lee-Yang zeros: a positive representation cannot exist everywhere in the neighborhood of such a zero. Simulation results raise the possibility that pattern-forming behavior may occur in finite density QCD in the vicinity of the critical line.

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Michael C. Ogilvie, Leandro Medina. 2018-11-27. Simulation of Scalar Field Theories with Complex Actions. https://arxiv.org/abs/1811.11112

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