Nonperturbative effects and long range order in the (2+1)-dimensional CP 1 model

Abstract

An explicit realization for time independent solitons with fractional magnetic flux in the 2+1 CP 1 model without Hopf term is discussed. It is shown that the gauge potential corresponding to this solution exactly coincides with the statistical field in the standard consideration. The corresponding solution in 1+1 physics (the so-called toron) has a finite action and is known to be responsible for the very important nonperturbative features of the two-dimensional model-confinement, right θ/ N dependence, the solution of the U(1) problem and so on…. An alternative mechanism of the anyonic attraction which could lead to formation of the boson from two different anyons is observed. It is shown that the Debye screening of a Coulomb-like interaction leads to a finite temperature phase transition at T= T c. The corresponding effective Landau-Ginsburg lagrangian at T< T c (when the molecu lar phase is realized) is obtained. The “almost long-range condensate” with power-law decay is constructed and the existence of the massless boson is observed. The possible relevance of this model to high temperature superconductivity is discussed.