O(2)-scaling in finite and infinite volume

Abstract

The exact nature of the chiral crossover in QCD is still under investigation. In $$N_\mathrm{f}=2$$Nf=2 and $$N_\mathrm{f}=(2+1)$$Nf=(2+1) lattice simulations with staggered fermions the expected O(N)-scaling behavior was observed. However, it is still not clear whether this behavior falls into the O(2) or O(4) universality class. To resolve this issue, a careful scaling and finite-size scaling analysis of the lattice results are needed. We use a functional renormalization group to perform a new investigation of the finite-size scaling regions in O(2)- and O(4)-models. We also investigate the behavior of the critical fluctuations by means of the 4th-order Binder cumulant. The finite-size analysis of this quantity provides an additional way for determining the universality class of the chiral transition in lattice QCD.