1998/07/01 by J. Kisker, Jens Kisker, A. P. Young
Mathematics · Medicine · Physics and Astronomy · #Condensed matter physics #Field (mathematics) #Ising model #Mathematics #Medicine #Opinion Dynamics and Social Influence #Physics #Quantum many-body systems #Random field #Statistical physics #Statistics #Theoretical and Computational Physics #Transverse field #Transverse plane #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.58.14397
published as Phys. Rev. B58, 14397 (1998) · 5 pages, 5 postscript figures included
arxiv created 1998/07/01 · openalex publication_date 1998/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the dynamical properties of the random transverse-field Ising chain at criticality using a mapping to free fermions with which we can obtain numerically exact results for system sizes L as large as 256. The probability distribution of the local imaginary time correlation function S(\ensuremathτ) is investigated and found to be simply a function of \ensuremathα\ensuremath≡\ensuremath-lnS(\ensuremathτ)/ln\ensuremathτ. This scaling behavior implies that the typical correlation function decays algebraically, Styp(\ensuremathτ)\ensuremath∼\ensuremathτ^\ensuremath-\ensuremathαtyp, where the exponent \ensuremathαtyp is determined from P(\ensuremathα), the distribution of \ensuremathα. The precise value for \ensuremathαtyp depends on exactly how the ``typical'' correlation function is defined. The form of P(\ensuremathα) for small \ensuremathα gives a contribution to the average correlation function Sav(\ensuremathτ) namely, Sav(\ensuremathτ)\ensuremath∼(ln\ensuremathτ)^\ensuremath-2xm, where xm is the bulk magnetization exponent, which was reported recently in Europhys. Lett. 39, 135 (1997). These results represent a type of ``multiscaling'' different from the well-known ``multifractal'' behavior.