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Two-point correlation function of an exclusion process with hole-dependent rates

Priyanka, P and Ayyer, Arvind and Jain, Kavita (2014) Two-point correlation function of an exclusion process with hole-dependent rates. In: PHYSICAL REVIEW E, 90 (6).

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Official URL: http://dx.doi.org/ 10.1103/PhysRevE.90.062104

Abstract

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n) = 1 + (b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b > 2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b - 2. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent nu = 1/(b - 2) for b < 3 and 1 for b > 3. These results are compared with those obtained using an exact series expansion for finite systems.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 21 Jan 2015 06:37
Last Modified: 21 Jan 2015 06:37
URI: http://eprints.iisc.ac.in/id/eprint/50730

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