Eur. Phys. J. B 13, 409-412 (2000)
https://doi.org/10.1007/s100510050050

Critical exponents of random XX and XY chains: Exact results via random walks

¹ FB 10.1 Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
² Laboratoire de Physique des Matériaux, Université Henri Poincaré, B.P. 239, 54506 Vandœvre lès Nancy Cedex, France
³ Institute for Theoretical Physics, Szeged University, 6720 Szeged, Hungary
⁴ Research Institute for Solid State Physics and Optics, 1525 Budapest, P.O. Box 49, Hungary

Received: 26 September 1999
Published online: 15 February 2000

Abstract

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent.