Journal of Experimental and Theoretical Physics

, Volume 95, Issue 3, pp 538–549 | Cite as

One-dimensional anisotropic Heisenberg model in the transverse magnetic field

  • D. V. Dmitriev
  • V. Ya. Krivnov
  • A. A. Ovchinnikov
  • A. Langari
Solids Electronic Properties

Abstract

The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.

Keywords

Anisotropy Ising Model Critical Exponent Field Dependence Conformal Invariance 
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Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • D. V. Dmitriev
    • 1
    • 2
  • V. Ya. Krivnov
    • 1
    • 2
  • A. A. Ovchinnikov
    • 1
    • 2
  • A. Langari
    • 2
    • 3
  1. 1.Joint Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia
  2. 2.Max-Planck-Institut für Physik Komplexer SystemeDresdenGermany
  3. 3.Institute for Advanced Studies in Basic SciencesZanjanIran

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