Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain

Details Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain

1998-11-26

arxiv.org/abs/cond-mat/9811369v1

Phys. Rev. B 59, 11308 (1999)

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages RevTeX, 8 eps-figures included

Scientific paper

10.1103/PhysRevB.59.11308

We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the non-linear susceptibility, higher excitations and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the average energy-density autocorrelations decay with another exponent as [G^e]_av(t)~t^{-2-1/z}.

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