Thermodynamic properties of the two-dimensional quantum Heisenberg ferromagnet and the effects of bond dilution.

Abstract

The energy, the specific heat, and the magnetic susceptibility of the bond-diluted S=(1/2) Heisenberg ferromagnet on a two-dimensional square lattice are studied using a Monte Carlo sampling of the terms contributing to the partition function. The full lattice is studied in detail for sizes up to 20\ifmmode\times\else\texttimes\fi{}20, and evidence is presented to suggest that the low-temperature correlation length behaves as \ensuremath{\xi}\ensuremath{\sim}${e}^{\ensuremath{\nu}\ensuremath{\beta}J}$ with \ensuremath{\nu}\ensuremath{\sim}1.91\ifmmode\pm\else\textpm\fi{}0.06. The temperature dependence of the susceptibility, however, is not quite a simple exponential in \ensuremath{\beta}J. Knowledge of the correlation length and finite-size scaling allows the determination of the prefactor. Our conclusion is that the low-temperature susceptibility behaves as ${T}^{\mathrm{\ensuremath{-}}1}$${e}^{2\ensuremath{\nu}\ensuremath{\beta}J}$. Square lattices of size ranging from 6\ifmmode\times\else\texttimes\fi{}6 to 12\ifmmode\times\else\texttimes\fi{}12 are studied for ${k}_{B}$T/J ranging from 0.1 to 3 and for several values of the bond probability p. Not surprisingly, the most drastic thermodynamic behavior near the critical bond-percolation probability is the sharp increase in the low-temperature susceptibility for p>${p}_{c}$. This corresponds to much larger correlation effects in the percolating lattice than below the percolation threshold. We also compare the thermodynamics at p=${p}_{c}$ to the scaling theories of Lubensky and Stanley et al. which suggest that the correlations at the percolation threshold are predominantly one dimensional.