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Analysis of the order parameter for uniform nearest particle system

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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.

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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

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  • DOI: https://doi.org/10.1007/BF01329859

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