Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model.

A perturbative method is developed to calculate the finite size corrections of the low lying energies of the asymmetric XXZ hamiltonian near the stochastic line. The crossover from isotropic to anisotropic, Kardar-Parisi-Zhang (KPZ) scaling of the mass gaps is determined in terms of universal crossover scaling functions. At the stochastic line, the asymmetric XXZ hamiltonian describes the time evolution of the single-step or body-centered solid-on-solid growth model in one dimension. The mass gaps of the growth model are found as a function of the growth rate and the substrate slope. Higher order corrections to the growth model mass gaps are also calculated to obtain the first terms of the KPZ to Edward-Wilkinson crossover scaling function in the large argument expansion in the zero slope sector.

• Publication year

  1995

• Venue

  Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

• Publication date

  1995-03-31

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PHYSREVE.52.3512arXiv cond-mat/9503169PMID 9963829
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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