Nonrenormalizability 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 moleculardynamics evolution on which the HMC algorithm is based. More precisely, studying the ϕ ^{4} theory, we find that the hyperbolic character of the moleculardynamics equations leads to nonlocal (and thus nonremovable) ultraviolet singularities already at oneloop order of perturbation theory.
 Publication:

Journal of High Energy Physics
 Pub Date:
 April 2011
 DOI:
 10.1007/JHEP04(2011)104
 arXiv:
 arXiv:1103.1810
 Bibcode:
 2011JHEP...04..104L
 Keywords:

 Lattice QCD;
 Lattice Quantum Field Theory;
 Renormalization Regularization and Renormalons;
 High Energy Physics  Lattice
 EPrint:
 Plain TeX source, 23 pages, 3 figures included