Effect of disorder on quantum phase transitions in anisotropicXYspin chains in a transverse field
- 1 July 1999
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 60 (1), 344-358
- https://doi.org/10.1103/physrevb.60.344
Abstract
We present some exact results for the effect of disorder on the critical properties of an anisotropic 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.
Keywords
This publication has 67 references indexed in Scilit:
- Non-Fermi Liquid Behavior and Griffiths Phase in-Electron CompoundsPhysical Review Letters, 1998
- Critical behavior at superconductor-insulator phase transitions near one dimensionPhysical Review B, 1998
- Magnetically mediated superconductivity in heavy fermion compoundsNature, 1998
- Nearly Singular Magnetic Fluctuations in the Normal State of a High- T c Cuprate SuperconductorScience, 1997
- Mean Field Theory of the Mott-Anderson TransitionPhysical Review Letters, 1997
- Continuous quantum phase transitionsReviews of Modern Physics, 1997
- Helium in AerogelPhysics Today, 1996
- The Anderson-Mott transitionReviews of Modern Physics, 1994
- Theory of Random MagnetsPhysics Today, 1988
- Nonanalytic Behavior Above the Critical Point in a Random Ising FerromagnetPhysical Review Letters, 1969