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Deconfinement critical point of heavy quark effective lattice theories

Effective three-dimensional Polyakov loop theories derived from QCD by strong coupling and hopping expansions are valid for heavy quarks and can also be applied to finite chemical potential $μ$, due to their considerably milder sign problem. We apply the Monte-Carlo method to the $N_f=1,2$ effective theories up to $\mathcal{O}(κ^4)$ in the hopping parameter at $μ=0$ to determine the critical quark mass, at which the first-order deconfinement phase transition terminates. The critical end point obtained from the effective theory to order $\mathcal{O}(κ^2)$ agrees well with 4-dimensional QCD simulations with a hopping expanded determinant by the WHOT-QCD collaboration. We also compare with full QCD simulations and thus obtain a measure for the validity of both the strong coupling and the hopping expansion in this regime.