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

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.

17 pages, 28 figures, version to appear in Physical Review D

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• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Machine learning phase transitions of the three-dimensional Ising universality class
• Scope and convergence of the hopping parameter expansion in finite temperature QCD with heavy quarks around the critical point
• Locating Critical Points Using Ratios of Lee-Yang Zeros
• Lee-Yang-zero ratio method in three-dimensional Ising model
• Canonical partition function and center symmetry breaking in finite density lattice gauge theories
• Finite-size effects and scaling properties of chiral and baryon-number fluctuations
• Phase structure of heavy dense lattice QCD and the three-state Potts model
• From lattice to observables: Real and virtual experiments for exploring hot and dense QCD