Cutoff effects in lattice actions at µ ≠ 0

Abstract

We look at the cutoff dependence of several lattice actions, including two improved actions viz. Naik and p4, and and chirally-invariant ones, namely fixed-point, overlap and domain-wall, with the aim of understanding its behavior at µ ≠ 0. Apart from numerical results, we also derive a series expansion in N ⁻¹ _r for the free-gas pressure. We find that actions with O(a ⁿ)-improved rotational invariance produce O(a ⁿ)-improvement in the pressure. The series for unimproved overlap and domain-wall fermions are identical to the naive series, and hence using Naik or p 4 kernels should produce improvement in these formulations as well. Lastly, we find that actions that are improved at µ = 0 remain so as the chemical potential is turned on. The series coefficients become µ-dependent now, however their functional form at any given order is the same for all actions.