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

A.P. Young

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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