Method to estimate critical exponents using numerical studies

Minerva Center and Department of Physics, Bar-Ilan University 52900 Ramat-Gan, Israel

Received: 3 August 2001
Accepted: 23 January 2002

Abstract

A novel method to estimate the critical point and critical exponents of physical models from numerical studies is presented. The method utilizes linear approximation to compute the values of the characteristic variables in the near vicinity of the critical point from numerical results obtained for only one point in that vicinity. The method is applied to two models: Two-dimensional directed percolation, and one-dimensional reaction-diffusion model. In both cases the critical point and critical exponents are determined with higher accuracy than achieved in former studies. In the reaction-diffusion model, the results strongly suggest simple rational values of 1/3, 1/12, etc., for the characteristic exponents.