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 ${{\chi }_{t}}=\langle {{Q}^{2}}\rangle /V$ does not scale properly in the continuum limit, i.e. that the quantity ${{\chi }_{t}}{{\xi }^{2}}$ diverges for ξ → ∞ (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.