Finite-size scaling around the critical point in the heavy quark region of QCD

TL;DR

This study investigates finite-size scaling near the critical point in heavy-quark QCD, demonstrating $Z(2)$ universality for large volumes and employing a hopping parameter expansion to efficiently perform large-volume simulations.

Contribution

It introduces a large-volume simulation approach using hopping parameter expansion and reweighting, clarifying the finite-size scaling behavior in heavy-quark QCD.

Findings

Binder cumulant follows $Z(2)$ scaling for $N_s/N_t extgreater= 9$

Binder cumulant becomes inconsistent with $Z(2)$ scaling for $N_s/N_t extless= 8$

Leading-order configurations effectively reduce statistical errors in reweighting

Abstract

Finite-size scaling is investigated in detail around the critical point in the heavy-quark region of nonzero temperature QCD. Numerical simulations are performed with large spatial volumes up to the aspect ratio $N_s/N_t=12$ at a fixed lattice spacing with $N_t=4$. We show that the Binder cumulant and the distribution function of the Polyakov loop follow the finite-size scaling in the $Z(2)$ universality class for large spatial volumes with $N_s/N_t \ge 9$, while, for $N_s/N_t \le 8$, the Binder cumulant becomes inconsistent with the $Z(2)$ scaling. To realize the large-volume simulations in the heavy-quark region, we adopt the hopping parameter expansion for the quark determinant: We generate gauge configurations using the leading order action including the Polyakov loop term for $N_t=4$, and incorporate the next-to-leading order effects in the measurements by the multipoint reweighting method. We find that the use of the leading-order configurations is crucially effective in suppressing the overlapping problem in the reweighting and thus reducing the statistical errors.