Geometric Algorithm for Abelian-Gauge Models

Abstract

Motivated by the sign problem in several systems, we have developed a geometric simulation algorithm based on the strong coupling expansion which can be applied to abelian pure gauge models. We have studied the algorithm in the U(1) model in 3 and 4 dimensions, and seen that it is practical and is similarly efficient to the standard heat-bath algorithm, but without the ergodicity problems which comes from the presence of vortices. We have also applied the algorithm to the Ising gauge model at the critical point, and we find hints of a better asymptotic behaviour of the autocorrelation time, which therefore suggests the possibility of a smaller dynamical critical exponent with respect to the standard heat-bath algorithm.

16 pages, 11 figures

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• Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• New developments for dual methods in lattice field theory at non-zero density
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory
• On the equation of state of U(1) lattice gauge theory in three dimensions
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$
• Approximate dual representation for Yang-Mills SU(2) gauge theory