## Finite Temperature and Dynamical
Properties of the Random Transverse-Field Ising Spin Chain

A.P. Young

**Abstract**

We study numerically the paramagnetic phase of the spin-1/2
random transverse-field
Ising chain, using a mapping to non-interacting
fermions. We extend our
earlier work, Phys. Rev. {\bf 53}, 8486 (1996), to finite
temperatures and to dynamical properties. Our results are consistent with the
idea that there are
``Griffiths-McCoy'' singularities in the paramagnetic phase
described by a continuously varying
exponent $z(\delta)$, where $\delta$ measures the deviation from criticality.
There are some discrepancies between the values of $z(\delta)$ obtained from
different quantities, but this may be due to corrections to scaling.
The {\em average} on-site
time dependent correlation function decays with a power law in the
paramagnetic phase, namely
$\tau^{-1/z(\delta)}$, where $\tau$ is imaginary time. However, the
{\em typical} value decays with a stretched exponential behavior,
$\exp(-c\tau^{1/\mu})$, where $\mu$ may be related to $z(\delta)$.
We also obtain results for the full probability distribution of time
dependent correlation functions at different points in the paramagnetic phase.

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