Monte Carlo simulation of CPN-1 models.

Abstract

Numerical simulations of two-dimensional ${\mathrm{CP}}^{N\ensuremath{-}1}$ models are performed at $N=2, 10, \mathrm{and} 21$. The lattice action adopted depends explicitly on the gauge degrees of freedom and shows precocious scaling. Our tests of scaling are the stability of dimensionless physical quantities (second moment of the correlation function versus inverse mass gap, magnetic susceptibility versus square correlation length) and rotation invariance. Topological properties of the models are explored by measuring the topological susceptibility and by extracting the Abelian string tension. Several different (local and nonlocal) lattice definitions of topological charge are discussed and compared. The qualitative physical picture derived from the continuum $\frac{1}{N}$ expansion is confirmed, and agreement with quantitative $\frac{1}{N}$ predictions is satisfactory. Variant (Symanzik-improved) actions are considered in the C${\mathrm{P}}^{1}$ \ensuremath{\cong} O(3) case and agreement with universality and previous simulations (when comparable) is found. The simulation algorithm is an efficient mixture of over-heat-bath and microcanonical algorithms. The dynamical features and critical exponents of the algorithm are discussed in detail.