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The beta function on a lattice is studied in SU(2) gluodynamics. The definition of the beta function within the scaling hypothesis at a finite lattice size is used. The functions obtained in this way are compared with the results known in the continuum limit. Graphics processing units are used as a computing platform, whereby a large amount of statistical data have been accumulated. Beta functions are analyzed for a large number of various lattices. It is shown that the beta function being studied complies with the respective analytic expression in the phase-transition region. A fast method that makes it possible to estimate the critical value of the coupling constant on a lattice is proposed. 相似文献