Do Instantons of the CP(N-1) Model Melt?

TL;DR

This paper investigates the behavior of instantons in the CP(N-1) model, revealing that at N=2 instantons tend to collapse, while at N=3,4 they remain mostly isolated with some overlap, shedding light on instanton dynamics.

Contribution

It provides a combined analytical and numerical study of instanton ensembles, highlighting how instanton behavior varies with N and the tendency for instantons to melt or remain distinct.

Findings

At N=2, instantons collapse into zero size.

At N=3,4, instantons are mostly isolated but some overlap occurs.

The study offers insights into the instanton melting phenomenon.

Abstract

In the two-dimensional CP(N-1) model one can parametrize exact many-instanton solutions via N `constituents' (called `zindons'). This parameterization allows, in principle, a complete `melting' of individual instantons. The model is therefore well suited to study whether dynamics prefers a dilute or a strongly overlapping ensemble of instantons. We study the statistical mechanics of instantons both analytically and numerically. We find that at N=2 the instanton system collapses into zero-size instantons. At N=3,4 we find that well-isolated instantons are dynamically preferred though 15-25% of instantons have a considerable overlap with others.