Correlation function and susceptibility of site- and bond-diluted Heisenberg paramagnets

Abstract

Generalizing the recent work of Collins, the wave-vector-dependent susceptibility and the static correlation function for a randomly diluted Heisenberg paramagnet on a Bravais lattice with quenched-site, or nearest-neighbor exchange-bond, dilution is studied by high-temperature series-expansion techniques. The first five coefficients for the spin correlation function $S\left(\overrightarrow{\mathrm{k}}\right)$ and susceptibility $\chi \left(\overrightarrow{\mathrm{k}}\right)$ are calculated for arbitrary $\overrightarrow{\mathrm{k}}$, the sign of the exchange and the spin magnitude and the magnetic site $c$ and bond $p$ concentrations. Numerical results for these functions are presented for various spins and for $\overrightarrow{\mathrm{k}}$ along the symmetry directions (1,1,1) and (1,0,0). Because of the generality of the present series, their length is rather limited, and as such they are not suitable for a careful analysis of the critical region. Nonetheless, to get a qualitative feel for the accuracy of the present results near the transition region, we have used Padé approximants for determining the correlation length $\xi \mathrm{}\left(T\right)\mathrm{}$ as a function of the reduced temperature $\epsilon =\frac{[T-T_{C\left(N\right)\mathrm{}}(\mathrm{random}\left)\right]}{T_{C\left(N\right)\mathrm{}}\left(\mathrm{random}\right)}$. In this manner, we estimate that the numerical accuracy of our results should be reasonable as long as the system is moderately above the transition temperature, e.g., $\epsilon \gtrsim 0.5$.