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We present calculations of the localisation length, $\lambda_{2}$, for twointeracting particles (TIP) in a one-dimensional random potential, presentingits dependence on disorder, interaction strength $U$ and system size.$\lambda_{2}(U)$ is computed by a decimation method from the decay of the Greenfunction along the diagonal of finite samples. Infinite sample size estimates$\xi_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduceapproximately the well-known dependence of the one-particle localisation lengthon disorder while for finite $U$, we find that $ \xi_{2}(U) \sim\xi_2(0)^{\beta(U)} $ with $\beta(U)$ varying between $\beta(0)=1$ and$\beta(1) \approx 1.5$. We test the validity of various other proposed fitfunctions and also study the problem of TIP in two different random potentialscorresponding to interacting electron-hole pairs. As a check of our method anddata, we also reproduce well-known results for the two-dimensional Andersonmodel without interaction.Comment: 34 RevTeX 3.0 pages with 16 figures include

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential