1998/12/31 by J. E. Bunder, Ross H. McKenzie · 3 citations
Materials Science · Mathematics · Medicine · Physics and Astronomy · #Anisotropy #Classical XY model #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Field (mathematics) #Magnetism in coordination complexes #Mathematics #Medicine #Organic and Molecular Conductors Research #Phase transition #Physics #Quantum #Quantum mechanics #Quantum phase transition #Spin (aerodynamics) #Transverse field #Transverse plane #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.60.344
published as Phys. Rev. B 60, 344 (1999). · 22 pages, RevTeX + epsf, 4 figures
arxiv created 1998/12/31 · openalex publication_date 1999/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse field. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse field then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRGDT and numerical work.