Year: 2011
Type: article
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 ϕ 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.
Source: Journal of High Energy Physics
Authors: Martin Lüscher, Stefan Schaefer
Institution: European Organization for Nuclear Research
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid:
OpenAlex ID: W2144755394