Energy-driven disorder in mean field QCD

An impact of the finite size effects on the vacuum free energy density of full QCD with $N_{\rm f}$ massless flavors in the presence of homogeneous (anti-)self-dual Abelian background gluon field is studied. The zero temperature free energy density of the four-dimensional spherical domain is computed as a function of the background field strength $B$ and domain radius $R$. Calculation is performed in the one-loop approximation improved by accounting for mixing of the quark and gluon quasi-zero modes with normal modes, with the use of the $\zeta$-function regularization. It is indicated that, under plausible assumption on the character of the mixing, the quantum correction to the free energy density has a minimum as a function of $B$ and $R$. Within the mean field approach to QCD vacuum based on domain wall network representation of the mean field, an existence of the minimum may prevent infinite growth of individual domain, thus protecting the vacuum from the long-range ordering, and, hence, serving as the origin of disorder in the statistical ensemble of domain wall networks, driven by the minimization of the overall free energy of the dominant gauge field configurations.