Progress in numerical simulations of systems with a $\theta -$vacuum like term: The two and three-dimensional Ising model within an imaginary magnetic field

Abstract

Using the approach developed in \cite{REFVIC2}, we succeeded in reconstructing the behaviour of the antiferromagnetic Ising model with imaginary magnetic field $i\theta$ for two and three dimensions in the low temperature regime. A mean-field calculation, expected to work well for high dimensions, is also carried out, and the mean-field results coincide qualitatively with those of the two- and three-dimensional Ising model. The mean field analysis reveals also a phase structure more complex than the one expected for $QCD$ with a topological $\theta -$therm.

21 pages, 15 figures. v2 added affiliation of the authors, corrected typos, largely improved presentation, corrected some plots. To be published in Nuclear Physics B

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• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
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Cited by in corpus (12)

• Approaches to the sign problem in lattice field theory
• Generalization of the Haldane conjecture to SU(3) chains
• The density of states approach to dense quantum systems
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations
• Massive Schwinger model at finite $\theta$
• Imaginary-field-driven phase transition for the $2$D Ising antiferromagnet: A fidelity-susceptibility approach
• Antiferromagnetic Ising model in an imaginary magnetic field
• A novel density of state method for complex action systems
• The density of states approach for the simulation of finite density quantum field theories
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$
• Ising ferromagnets and antiferromagnets in an imaginary magnetic field