Analysis of the order parameter for uniform nearest particle system |
| |
Authors: | Norio Konno Makoto Katori |
| |
Institution: | (1) Department of General Education, Muroran Institute of Technology, Mizumoto-cho, Muroran, 050 Hokkaido, Japan;(2) Department of Physics, Faculty of Science, University of Tokyo, Bunkyo-ku, 113 Tokyo, Japan |
| |
Abstract: | The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space
. The rigorous upper bound
(mf)
= ( – 1)/ for the order parameter
2, is given by the correlation identity and the FKG inequality. Then an improvement of this bound
(mf)
is shown in a similar fashion;
C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense. |
| |
Keywords: | Uniform nearest particle system order parameter critical value critical exponent correlation identities the FKG inequality |
本文献已被 SpringerLink 等数据库收录! |
|