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We calculate exactly functional determinants for quantum oscillations about periodic instantons with a nontrivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with nontrivial holonomy occur in the Yang-Mills partition function. The weight depends on the value of the holonomy, the temperature, ₐ₂₃, and the separation between the BPS monopoles (or dyons) that constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times a definite interaction energy. We present an argument that at temperatures below a critical one related to ₐ₂₃, trivial holonomy is unstable, and that calorons ``ionize'' into separate dyons.
Diakonov et al. (Tue,) studied this question.