Hyperscaling for Oriented Percolation in 1+1 Space–Time Dimensions

Journal Article · Tue May 15 04:00:00 EDT 2018 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/S10955-018-2020-2· OSTI ID:22788172

Sakai, Akira ^[1]

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1. Hokkaido University, Department of Mathematics (Japan)

Consider nearest-neighbor oriented percolation in d+1 space–time dimensions. Let ρ,η,ν be the critical exponents for the survival probability up to time t, the expected number of vertices at time t connected from the space–time origin, and the gyration radius of those vertices, respectively. We prove that the hyperscaling inequality dν≥η+2ρ, which holds for all d≥1 and is a strict inequality above the upper-critical dimension 4, becomes an equality for d=1, i.e., ν=η+2ρ, provided existence of at least two among ρ,η,ν. The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin et al. [6].

• OSTI ID: 22788172
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 3 Vol. 171; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIMENSIONS
PROBABILITY
SCALING LAWS
SPACE-TIME