Scaling functions of the three-dimensional $Z(2)$, $O(2)$ and $O(4)$ models and their finite size dependence in an external field

Abstract

We analyze scaling functions in the $3$-$d$, $Z(2)$, $O(2)$ and $O(4)$ universality classes and their finite size dependence using Monte Carlo simulations of improved ${\varphi }^4$ models. Results for the scaling functions are fitted to the Widom-Griffiths form, using a parametrization also used in analytic calculations. We find good agreement on the level of scaling functions and the location of maxima in the universal part of susceptibilities. We also find that an earlier parametrization of the $O(4)$ scaling function, using 14 parameters, is well reproduced when using the Widom-Griffiths form with only three parameters. We furthermore show that finite size corrections to the scaling functions are distinctively different in the $Z(2)$ and $O(N)$ universality classes and determine the volume dependence of the peak locations in order parameter and mixed susceptibilities.

arXiv comment15 pages, 8 figures, accepted version

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Cited by in corpus (5)

• Soft modes in hot QCD matter
• Curvature of the chiral phase transition line from the magnetic equation of state of (2+1)-flavor QCD
• Lee-Yang and Langer edge singularities from analytic continuation of scaling functions
• Variations of the crossover and first-order phase transition curve in modeling the QCD equation of state
• Towards a parameter-free analysis of the QCD chiral phase transition and its universal critical behavior