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The beta-function is investigated on the lattice in SU(2) gluodynamics. It isdetermined within a scaling hypothesis while a lattice size fixed to be takeninto account. The functions calculated are compared with the ones obtained inthe continuum limit. Graphics processing units (GPU) are used as a computingplatform that allows gathering a huge amount of statistical data. Numerousbeta-functions are analyzed for various lattices. The coincidence of thelattice beta-function and the analytical expression in the region of the phasetransition is shown. New method for estimating a critical coupling value isproposed.

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