arXiv subjects

Ilya O. Sandoval

Publications and source records attributed to Ilya O. Sandoval.

3 recordsLinked to original sources

arXiv2018

Topological Susceptibility of the 2d O(3) Model under Gradient Flow

The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological sectors. Topology can also be defined in its lattice regularised version, but semi-classical arguments suggest that the topological susceptibility $χ_{\rm t}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity $χ_{\rm t}\, ξ^{2}$ diverges at large correlation length $ξ$. Here we investigate the question whether or not this divergence persists when the configurations are smoothened by the Gradient Flow (GF). The GF destroys part of the topological windings; on fine lattices this strongly reduces $χ_{\rm t}$. However, even when the flow time is so long that the GF impact range --- or smoothing radius --- attains $ξ/2$, we do still not observe evidence of continuum scaling.

hep-lat↗

arXiv2017

Topological Susceptibility under Gradient Flow

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $χ_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates $χ_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $ξ^{2}$). This ongoing study is based on direct measurements of $χ_{\rm t}$ in $L \times L$ lattices, at $L/ξ\simeq 6$.

hep-lat↗

arXiv2017

Topology in the 2d Heisenberg Model under Gradient Flow

The 2d Heisenberg model --- or 2d O(3) model --- is popular in condensed matter physics, and in particle physics as a toy model for QCD. Along with other analogies, it shares with 4d Yang-Mills theories, and with QCD, the property that the configurations are divided in topological sectors. In the lattice regularisation the topological charge $Q$ can still be defined such that $Q \in \mathbb{Z}$. It has generally been observed, however, that the topological susceptibility $χ_{\rm t} = \langle Q^2 \rangle / V$ does not scale properly in the continuum limit, i.e. that the quantity $χ_{\rm t} ξ^2$ diverges for $ξ\to \infty$ (where $ξ$ is the correlation length in lattice units). Here we address the question whether or not this divergence persists after the application of the Gradient Flow.

hep-lat↗