Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Fisher’s [Phys. Rev. B (formula presented) 6411 (1995)] real-space renormalization-group (RG) treatment of random transverse-field Ising spin chains is extended into the strongly ordered and strongly disordered Griffiths phases, and asymptotically exact results are obtained. In the noncritical region the asymmetry of the renormalization of the couplings and the transverse fields is related to a nonlinear quantum control parameter Δ, which is a natural measure of the distance from the quantum critical point. Δ, which is found to stay invariant along the RG trajectories, and has been expressed by the initial disorder distributions, stands in the singularity exponents of different physical quantities (magnetization, susceptibility, specific heat, etc.), which are exactly calculated. In this way we have observed a weak-universality scenario: the Griffiths-McCoy singularities do not depend on the form of the disorder, provided the nonlinear quantum control parameter has the same value. The exact scaling function of the magnetization with a small applied magnetic field is calculated, and the critical point magnetization singularity is determined in a simple, direct way.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume65
Issue number6
DOIs
Publication statusPublished - Jan 1 2002

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Fingerprint Dive into the research topics of 'Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases'. Together they form a unique fingerprint.

  • Cite this