501 A new procedure of numerical simulation by the Parisi-Wu stochastic quantization method is proposed to obtain long-range correlations and energy gaps. We first observe that the original Parisi's procedure of numerical simulation can give us a remarkable merit for a fixed potential model and the O(N 2:4) nonlinear a-model but not so much for the 0(3) nonlinear a-model; in comparison with the conventional Monte Carlo methods based on path integral formulas. Examining behaviors of correlation

more »

... unctions in updating processes, we find that the situation is much improved if the external source to generate correlation functions in its linear response is switched on after reaching thermal equilibrium, and even more if this swithcing-on procedure is appropriately repeated several times. In fact, the new procedure enables us to obtain correlation functions covering the whole lattice region and correspondingly accurate energy gaps, through updation steps much smaller than by the conventional Monte Carlo methods, in the case of 0(3) nonlinear a-model on a 12 x 12 and a 20 x 20 lattices while those obtained by the original Parisi's procedure of the stochastic quantization or by the conventional Monte Carlo cover only a few sites as is well known. Even in the scaling region (fl = 1.5) the new procedure gives correlation functions covering about 20 sites and corresponding mass gap mg/ AL = 110 ±5 for the lattice with 50X50 sites. § 1. Introduction Through recent works we have seen remarkable merits of the Parisi-Wu stochastic quantization method (abbreviated as SQM in what follows) applied to gauge fields and other theoretical problems. l ) In order to develop non-perturbative approach, in previous papers,2) we formulated a general theory of SQM for a dynap1ical system with regular Lagrangian under holonomic constraints, and applied it to numerical simulations of internal energy in the case of two-dimensional O(N) nonlinear6-model. In this paper we present a new procedure of numerical simulation by SQM which enables us to obtain long-range correlations and energy gaps or hadron masses. As is widely known, it is not so easy to obtain long-range correlations by means of the conventional Monte Carlo methods (e.g., the Metropolis method) based on path integral formulas. To improve this situation, Parisi proposed a special procedure of numerical simulation within the framework of SQM, and applied it to several problems such as a linear chain model, the two-dimensional O(N) nonlinear 6-model and the fourdimensional SU(2) gauge theory.3) He and his collaborators obtained rather beautiful results except in the case of the 0(3) nonlinear 6-model. One of the essential features of his procedure is to use the same series of random sources in the fundamental Langevin equations for the corresponding updation processes both of a dynamical quantity and of the same one modified by a small external source so introduced as to generate the *) Present address: