P o S(LATTICE 2007)198 Finite Size Scaling for the O(N) universality class from Renormalization Group Methods

The QCD phase diagram at finite temperature and density is a topic of considerable interest. Although much progress has been made in recent years, some open questions remain. Even at zero density, the order of the transition for two light flavors of fermions has not yet been conclusively established. While considerable evidence exists in favor of a second-order transition for massless quarks and a crossover for massive quarks, some recent results with two flavors of staggered fermions suggest a transition of first order. Since lattice simulations are performed in finite simulation volumes, actual phase transitions can-not be observed directly. Thus, finite-size scaling is a very useful tool in the analysis of lattice data. By comparing the scaling behavior of observables to the expected scaling properties, values of critical exponents can be confirmed and the order as well as the universality class of a transi-tion can be established. In the comparison to lattice QCD results, the critical exponents and the universal scaling functions have been obtained mainly by means of lattice simulations of O(N) spin models, and results are usually restricted to the critical temperature or the point at which the susceptibilities peak. We propose to use a non-perturbative Renormalization Group method for this purpose. We hav