On the questions of phase transition and coupling constant renormalization in the interacting instanton gas

Properties of the Yang-Mills instanton gas give rise at least to two effects: a first order phase transition bag-to-vacuum driven by a classical external field and a non-perturbative renormalization of the coupling constant at large distances. The aim of the paper is to check both conjectures by considering the statistical mechanics of the interacting instanton gas. The consideration is based on the dilute gas approximation involving Gaussian integration over fluctuations around superpositions of instantons and antiinstantons. It is shown that the allowance for interactions does not qualitatively affect the instanton related rise of the #betta# function in the interpolation region. The existence of a mechanism restricting more drastically the length scale where instanton calculations can be applied is indicated