On Statistical Mechanics of Instantons in the CPNc-1 Model
Abstract
We introduce an explicit form of the multi-instanton weight including also instanton--anti-instanton interactions for arbitrary Nc in the two-dimensional CPNc-1 model. To that end, we use the parametrization of multi-instantons in terms of instanton `constituents' which we call `zindons' for short. We study the statistical mechanics of zindons analytically (by means of the Debye-H\"uckel approximation) and numerically (running a Metropolis algorithm). Though the zindon parametrization allows for a complete `melting' of instantons we find that, through a combination of dynamical and purely geometric factors, a dominant portion of topological charge is residing in well-separated instantons and anti-instantons.
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