39 research outputs found
Universality of the topological susceptibility in the SU(3) gauge theory
The definition and computation of the topological susceptibility in
non-abelian gauge theories is complicated by the presence of non-integrable
short-distance singularities. Recently, alternative representations of the
susceptibility were discovered, which are singularity-free and do not require
renormalization. Such an expression is here studied quantitatively, using the
lattice formulation of the SU(3) gauge theory and numerical simulations. The
results confirm the expected scaling of the susceptibility with respect to the
lattice spacing and they also agree, within errors, with computations of the
susceptibility based on the use of a chiral lattice Dirac operator.Comment: Plain TeX source, 14 pages, 1 figure; v3: further typos corrected,
version published in JHE
Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
We study a variant of the cyclic Lotka-Volterra model with three-agent
interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors
game, the model describes an ideal ecosystem in which cyclic competition among
three species develops through cooperative predation. Its rate equations in a
well-mixed environment display a degenerate Hopf bifurcation, occurring as
reactions involving two predators plus one prey have the same rate as reactions
involving two preys plus one predator. We estimate the magnitude of the
stochastic noise at the bifurcation point, where finite size effects turn
neutrally stable orbits into erratically diverging trajectories. In particular,
we compare analytic predictions for the extinction probability, derived in the
Fokker-Planck approximation, with numerical simulations based on the Gillespie
stochastic algorithm. We then extend the analysis of the phase portrait to
heterogeneous rates. In a well-mixed environment, we observe a continuum of
degenerate Hopf bifurcations, generalizing the above one. Neutral stability
ensues from a complex equilibrium between different reactions. Remarkably, on a
two-dimensional lattice, all bifurcations disappear as a consequence of the
spatial locality of the interactions. In the second part of the paper, we
investigate the effects of mobility in a lattice metapopulation model with
patches hosting several agents. We find that strategies propagate along the
arms of rotating spirals, as they usually do in models of cyclic dominance. We
observe propagation instabilities in the regime of large wavelengths. We also
examine three-agent interactions inducing nonlinear diffusion.Comment: 22 pages, 13 figures. v2: version accepted for publication in EPJ
Fluctuations and reweighting of the quark determinant on large lattices
We propose to stabilise HMC simulations of lattice QCD with very light Wilson
quarks by splitting the quark determinant into two factors and by treating the
factor that includes the contribution of the low modes of the Dirac operator as
a reweighting factor. In general, determinant reweighting becomes inefficient
on large lattices, because the statistical fluctuations of quark determinants
increase exponentially with the lattice volume. Random matrix theory and some
numerical studies now suggest that the low-mode contribution to the determinant
behaves differently, which allows factorisations to be devised that preserve
the efficiency of the simulation on large lattices.Comment: 7 pages, talk presented at the XXVI International Symposium on
Lattice Field Theory, July 14-19, 2008, Williamsburg, Virginia, US
A perturbative approach to the reconstruction of the eigenvalue spectrum of a normal covariance matrix from a spherically truncated counterpart
In this paper we propose a perturbative method for the reconstruction of the
covariance matrix of a multinormal distribution, under the assumption that the
only available information amounts to the covariance matrix of a spherically
truncated counterpart of the same distribution. We expand the relevant
equations up to the fourth perturbative order and discuss the analytic
properties of the first few perturbative terms. We finally compare the proposed
approach with an exact iterative algorithm (presented in Palombi et al. (2017))
in the hypothesis that the spherically truncated covariance matrix is estimated
from samples of various sizes.Comment: 39 pages, 7 figures. v2: version accepted for publication in J. Comp.
Appl. Mat
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by non-perturbatively improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered