Non-renormalizability of the HMC algorithm

Abstract

In lattice field theory, renormalizable simulation algorithms are attractive, because their scaling behaviour as a function of the lattice spacing is predictable. Algorithms implementing the Langevin equation, for example, are known to be renormalizable if the simulated theory is. In this paper we show that the situation is different in the case of the molecular-dynamics evolution on which the HMC algorithm is based. More precisely, studying the phi^4 theory, we find that the hyperbolic character of the molecular-dynamics equations leads to non-local (and thus non-removable) ultraviolet singularities already at one-loop order of perturbation theory.

Plain TeX source, 23 pages, 3 figures included; v2: typos corrected, agrees with published version

References in corpus (6)

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• Critical slowing down and error analysis in lattice QCD simulations
• Theta dependence of SU(N) gauge theories
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Cited by in corpus (14)

• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Lattice QCD without topology barriers
• Studying the gradient flow coupling in the Schrödinger functional
• The gradient flow coupling in the Schrödinger Functional
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• Stochastic locality and master-field simulations of very large lattices
• Step scaling and the Yang-Mills gradient flow
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Influence of topology on the scale setting
• Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory
• Polynomial Filtered HMC -- an algorithm for lattice QCD with dynamical quarks
• Testing algorithms for critical slowing down
• Topology changing update algorithms for SU(3) gauge theory
• Markovian versus non-Markovian stochastic quantization of a complex-action model