On Statistical Mechanics of Instantons in the CP^{N_c-1} Model

Details On Statistical Mechanics of Instantons in the CP^{N_c-1} Model On Statistical Mechanics of Instantons in the CP^{N_c-1} Model

1999-09-13

arxiv.org/abs/hep-th/9909078v1

Nucl.Phys. B571 (2000) 91-119

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, LaTeX

Scientific paper

10.1016/S0550-3213(99)00756-7

We introduce an explicit form of the multi-instanton weight including also instanton--anti-instanton interactions for arbitrary $N_c$ in the two-dimensional $CP^{N_c-1}$ 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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