2001/08/22 by Ferenc Iglói · 6 citations
Physics and Astronomy · #Quantum many-body systems #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.65.064416
published as Phys. Rev. B65, 064416 (2002) · 11 pages
arxiv created 2001/08/22 · openalex publication_date 2002/01/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fisher's [Phys. Rev. B 51, 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 \ensuremathΔ, which is a natural measure of the distance from the quantum critical point. \ensuremathΔ, 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.