Prog. Theor. Phys. Vol. 76 No. 2 (1986) pp. 501-511

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New Procedure of Numerical Simulation of Long-Range Correlations and Energy Gaps by Stochastic Quantization

— Fixed Potential Model and O(3) Nonlinear σ-Model —

Mikio Namiki, Ichiro Ohba, Keisuke Okano, Masanori Rikihisa and Satoshi Tanaka

Department of Physics, Waseda University, Tokyo 160

(Received December 12, 1985)

Abstract:

A new procedure of numerical simulation by the Parisi-Wu stochastic quantization method is propoesed 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≥4) nonlinear σ-model but not so much for the O(3) nonlinear σ-model, in comparison with the conventional Monte Carlo methods based on path integral formulas. Examining behaviors of correlation functions 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 switching-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 O(3) nonlinear σ-model on a 12 ×12 and a 20 ×20 lattices while those obtained by the original Parisi's procedure of the stochastic quanization or by the onventional Monte Carlo cover only a few sites as is well known. Even in the scalling region (β=1.5) the new procedure gives correlation functions covering about 20 sites and corresponding mass gap m_g/Δ_L=110 ±5 for the lattice with 50 ×50 sites.

URL : http://ptp.ipap.jp/link?PTP/76/501/
DOI : 10.1143/PTP.76.501

References:

D. Zwanziger, Nucl. Phys. B192 (1981), 259[Elsevier].
L. Baulieu and D. Zwanziger, Nucl. Phys. B193 (1981), 163[Elsevier].
M. Namiki, I. Ohba, K. Okano and Y. Yamanaka, Prog. Theor. Phys. 69 (1983), 1580[PTP].
H. Nakazato, M. Namiki, I. Ohba and K. Okano, Prog. Theor. Phys. 70 (1983), 298[PTP].
E. Floratos and J. Illiopoulous, Nucl. Phys. B214 (1983), 392[Elsevier].
T. Fukai, H. Nakazato, I. Ohba, K. Okano and Y. Yamanaka, Prog. Theor. Phys. 69 (1983), 361[PTP].
M. Namiki and Y. Yamanaka, Prog. Theor. Phys. 69 (1983), 1764[PTP].
A. Guha and S. -C. Lee, Phys. Lett. 134B (1984), 216.
T. Fukai and K. Okano, Prog. Theor. Phys. 73 (1985), 790[PTP].
M. Namiki, I. Ohba and K. Okano, Prog. Theor. Phys. 72 (1984), 350[PTP].
M. Namiki, I. Ohba, K. Okano, M. Rikihisa and S. Tanaka, Prog. Theor. Phys. 73 (1985), 186[PTP].
G. Parisi, Nucl. Phys. B180 (1981), 378[Elsevier]; ibid. B205 (1982), 337[Elsevier]; Preprint LNF-83/35(p).
M. Falcioni, E. Marinari, M. L. Paciello, G. Parisi, B. Taglienti and Zhang Yi-Cheng, Nucl. Phys. B215 (1983), 265[Elsevier].
I. T. Drummond, S. Duane and R. R. Horgan, Nucl. Phys. B220 (1983), 119[Elsevier].
S. H. Shenker and J. Tobochnik, Phys. Rev. B22 (1980), 4462[APS].
G. Martinelli, G. Parisi and R. Petronzio, Phys. Lett. 100B (1981), 485.
G. Fox, R. Gupta, O. Martin and S. Otto, Nucl. Phys. B205 (1982), 412[Elsevier].
M. Fukugita and Y. Oyanagi, Phys. Lett. 123B (1983), 71.
M. Falcioni, G. Martinelli and G. Parisi, Nucl. Phys. B225 (1983), 313[Elsevier].
S. Itoh, Y. Iwasaki and T. Yoshie, Nucl. Phys. B250(1985), 312[Elsevier].
H. Arisue, Phys. Lett. 140B (1984), 383.
B. Berg, DESY Preprint, 83-031 (1983).
R. Gupta, Preprint, CALT-68-1010 (1983).
J. Shigemitsu and J. B. Kogut, Nucl. Phys. B190 (1981), 365[Elsevier].

Citing Article(s) :

Progress of Theoretical Physics Vol. 76 No. 3 (1986) pp. 708-714 :
Possible Derivation of Energy Gaps or Hadron Masses from Fictitious-Time Correlations in Stochastic Quantization Method

Norio Nakazato, Mikio Namiki and Hiroyuki Shibata