Papers › Topological charge using cooling and the gradient flow
Topological charge using cooling and the gradient flow
Constantia Alexandrou, Andreas Athenodorou, Karl Jansen
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The equivalence of cooling to the gradient flow when the cooling step n_c and the continuous flow step of gradient flow τ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate n_c and τ and show that the results for the topological charge become equivalent when rescaling τ≃n_c/(3-15 c₁) where c₁ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with N_f=2+1+1 twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling τ≃n_c/(3-15 c₁) leads to equivalent results.
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