Numerical simulations of the O(3) and CP1 models using the Langevin equations and the Metropolis algorithm

Abstract

We test a proposal by Namiki and collaborators to enforce constraints on Langevin equations and Parisi's technique to calculate correlation functions via Langevin equations. The numerical study of the equivalence between the O(3) model and the bound state of the pure CP1 model, which can be demonstrated analytically, is used to measure the performance of these methods. In particular, as expected, we show that (a) the relations gO(3)=2gCP1 and EO(3)=2ECP1+2 for the couplings and energies hold beyond the classical level and (b) the mass gap as a function of the coupling is the same for both models. In addition we calculate the mass gap for the CP1 model minimally coupled to fermions. All results are compared with those obtained using the multihit Metropolis algorithm. © 1990 The American Physical Society.