Two-dimensional isotropic orientational glasses: a computer-simulation study

The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction.It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to ferromagnetic correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT0, and the critical exponents for this zero-temperature phase transition are estimated.Dynamic correlation functions are analyzed as well and it is shown that the dacay of spatially displaced correlations displays a Kohlrausch-Williams-Watts behavior similar to the self-correlation function of the quadrupole moments.Some quantities are compared to their corresponding counterparts on the threedimensional simple cubic lattice, which also has a zero-temperature transition but at corresponding temperatures has stronger short-range-order.