Showing papers by "Nikolaus Rajewsky published in 2000"
TL;DR: In this paper, the stationary state of a simple exclusion process on a ring was studied and it was shown that in the framework of a grand canonical ensemble there is no phase transition from a mixed phase to a disordered phase.
Abstract: We study the stationary state of a simple exclusion process on a ring which was recently introduced by Arndt et al. (J. Phys. A 31 (1998) L45; J. Stat. Phys. 97 (1999) 1). This model exhibits spatial condensation of particles. It has been argued (J. Phys. A 31 (1998) L45; cond-mat/9809123) that the model has a phase transition from a “mixed phase” to a “disordered phase”. However, in this paper exact calculations are presented which, we believe, show that in the framework of a grand canonical ensemble there is no such phase transition. An analysis of the fluctuations in the particle density strongly suggests that the same result also holds for the canonical ensemble and suggests the existence of extremely long (but finite) correlation lengths (for example 1070 sites) in the infinite system at moderate parameter values in the mixed regime.
78 citations
TL;DR: This paper reconsiders a deterministic version of the BTW model, where sand grains are added always to one fixed site on the square lattice, and using the Abelian sandpile formalism discusses the static properties of the system.
Abstract: The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice.
7 citations