A high statistics study of the beta-function in the SU(2) lattice thermodynamics

The beta-function is investigated on the lattice in SU(2) gluodynamics. It is determined within a scaling hypothesis while a lattice size fixed to be taken into account. The functions calculated are compared with the ones obtained in the continuum limit. Graphics processing units (GPU) are used as a computing platform that allows gathering a huge amount of statistical data. Numerous beta-functions are analyzed for various lattices. The coincidence of the lattice beta-function and the analytical expression in the region of the phase transition is shown. New method for estimating a critical coupling value is proposed.