Glassy dynamics and aging in an exactly solvable spin model

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 5, 1999, Pages 5068-5072

  Newman, M E J ^a   Moore, Cristopher ^a  

^a SANTA FE INSTITUTE   (Mexico)

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ARTICLE;

EID: 0001072821     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.5068     Document Type: Article

References (21)

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18. Since Eq. (7) is the rule for iterating a certain additive cellular automaton in one dimension, we can count ground states with periodic boundary conditions by counting periodic orbits of this cellular automaton. The number of orbits as a function of lattice size turns out to have interesting number-theoretic properties, and has been studied by O. Martin, A. M. Odlyzko, and S. Wolfram, Commun. Math. Phys. 93, 219 (1984).
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20. The set of local minima in our model is the same as the set of allowed states of Baxter’s hard-hexagon model [R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982)]. However, the cooling process creates spatial correlations, giving an entropy at (Formula presented) lower than that of Baxter’s model.
21. We can generalize this to higher dimensions. For example, in (Formula presented) the excitations of a model with four-spin interactions on tetrahedra of one orientation on a fcc lattice will be tetrahedra of size (Formula presented) with energy barriers (Formula presented) A model with interactions on both kinds of tetrahedra is discussed in Ref. 10.