1105.0584 (Juergen Engels et al.)

The scaling functions of the free energy density and its derivatives for
the 3d O(4) model    [PDF]

Juergen Engels, Frithjof Karsch

We derive direct representations of the scaling functions of the 3d O(4)
model which are relevant for comparisons to other models, in particular QCD.
This is done in terms of expansions in the scaling variable z= t/h^{1/Delta}.
The expansions around z=0 and the corresponding asymptotic ones for z --> +-
infinity overlap such that no interpolation is needed. The expansion
coefficients are determined numerically from the data of a previous high
statistics simulation of the O(4) model on a three-dimensional lattice of
linear extension L=120. From the scaling function of the magnetization we
calculate the leading asymptotic coefficients of the scaling function of the
free energy density. As a result we obtain the universal amplitude ratio
A^+/A^-=1.84(4) for the specific heat. Comparing the scaling function of the
energy density to the data we find the non-singular part of the energy density
epsilon_{ns}(T) with high precision and at the same time excellent scaling
properties.

View original: http://arxiv.org/abs/1105.0584