2011/05/31 by J. Engels, Juergen Engels, Frithjof Karsch +1 · 3 citations
Mathematics · Physics and Astronomy · #Amplitude #Energy (signal processing) #Function (biology) #Geometry #High-Energy Particle Collisions Research #Invertible matrix #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scaling #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1103/physrevd.85.094506
24 pages, 10 figures, extended discussion on regular term and corrections to scaling, references added
arxiv created 2012/02/22 · openalex publication_date 2012/05/21 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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/\ensuremathΔ. The expansions around z=0 and the corresponding asymptotic ones for z\ensuremath→\ifmmode±\else\textpm\fi\ensuremath∞ 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^\ensuremath-=1.84(4) for the specific heat. Comparing the scaling function of the energy density to the data we find the nonsingular part of the energy density ϵns(T) with high precision and at the same time excellent scaling properties.