Abstract
The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space\(\left\{ {0, 1} \right\}^{z^1 } \). The rigorous upper boundρ (mf) λ = (λ − 1)/λ for the order parameterρ 2, is given by the correlation identity and the FKG inequality. Then an improvement of this boundρ (mf) λ is shown in a similar fashion;ρ λ ⩽C(λ − 1)/|log(λ − 1) for λ>1. Recently, Mountford proved that the critical value λc=1. Combining his result and our improved bound implies that if the critical exponentβ exists, it is strictly greater than the mean-field value 1 in the weak sense.
Similar content being viewed by others
References
T. M. Liggett,Interacting Particle Systems (Springer-Verlag, New York, 1985).
T. S. Mountford, The critical value for the uniform nearest particle process, Preprint (1990).
N. Konno and M. Katori, Correlation identities for nearest-particle systems and their applications to one-dimensional contact process,Mod. Phys. Lett. B 5:151–159 (1991).
N. Konno and M. Katori, Applications of the Harris-FKG inequality to upper bounds for order parameters in the contact processes,J. Phys. Soc. Jpn. 60:430–434 (1991).
H. Kesten and Y. Zang, Strict inequalities for some critical exponents in two-dimensional percolation,J. Stat. Phys. 46:1031–1055 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Konno, N., Katori, M. Analysis of the order parameter for uniform nearest particle system. J Stat Phys 65, 247–254 (1991). https://doi.org/10.1007/BF01329859
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01329859