Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size

Details Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size

1999-04-09

arxiv.org/abs/cond-mat/9904130v1

Phys. Rev. E Vol. 60 pg. 79-88 (1999)

Physics

Condensed Matter

Statistical Mechanics

28 pages, 2 figures. To appear in Phys. Rev. E (1999)

Scientific paper

10.1103/PhysRevE.60.79

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes $s = 0,1,2,...$, in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of molecules's sizes may change the excluded volume almost continuously. We solve the model exactly through the Bethe ansatz and the dynamical critical exponent $z$ is calculated from the finite-size corrections of the mass gap of the related quantum chain. Our results show that for an arbitrary distribution of molecules the dynamical critical behavior is on the Kardar-Parizi-Zhang (KPZ) universality.

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