On the statistical mechanics of dense instanton gases

Instanton gases of two-dimensional?P ^n?1 and four-dimensionalSU(n) Yang-Mills theories are considered. The presumable denseness of instanton gases in these models and the corresponding statistics of instantons lead to a theormodynamic limit in which the coupling constant dependence of non-perturbative quantities is modified by a factor proportional to 1/n compared to the case of a dilute gas. As a consequence the largen limit and the infinite volume limit do not appear to commute. We present a naive droplet model for dense instanton gases which exhibits these features. Possible consequences for the large order behaviour of perturbation series are discussed.