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Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
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Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from stochastic quantisation (or complex Langevin dynamics) in the case of a simple model and contrast the distributions being sampled. We also study the role of the residual phase on the Lefschetz thimble.
Forward citations
Cited by 3 Pith papers
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Complex Langevin results in one- and two-dimensional toy models match a linear combination of integration cycles when boundary terms vanish, and the kernel choice controls which cycles contribute.
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For the 2d negative-coupling O(N) model at large N, the correct vacuum is a saddle point on a non-principal Riemann sheet, giving a real free energy and dynamical stability at all temperatures.
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Combining complex Langevin dynamics with score-based and energy-based diffusion models
Energy-based diffusion models trained on complex Langevin data produce an explicit energy function for the sampled distribution, enabling MCMC without re-simulation.
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