Exact enumeration of the Critical States in the Oslo Model

2002/03/12 by Alvin Chua, Alvin L.-S. Chua, Chua, Alvin +2 · 1 citation
Chemistry · Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Graph Theory Research #Condensed Matter (cond-mat) #FOS: Physical sciences #Game Theory and Voting Systems #History and advancements in chemistry #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/0203260

11 pagers, 4 figures, 6 files in all. Apologies for equations in abstract. Submitted to PRL

openalex publication_date 2002/03/12 · arxiv created 2002/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine analytically the number N_R(L) of recurrent states in the 1d Oslo model as a function of system size L. The solution N_R(L) = (1+√(5))/(2√(5))((3+√(5))/(2))^L + (√(5)-1)/(2√(5))((3-√(5))/(2))^L is in exact agreement with the number enumerated in computer simulations for L = 1 - 10. For L ≫ 1, the number of allowed metastable states in the attractor increases exponentially as N_R(L) ≈ c₊ λ₊^L, where λ₊ = (3+√(5))/(2) is the golden mean. The system is non-ergodic in the sense that the states in the attractor are not equally probable.

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• An explicit formula of the Oslo stationary state

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