Transmission of order in some unusual dilute systems

Abstract

As a system is diluted, the critical temperature $T_c$ may fall to zero at a concentration $x_c$ greater than the percolation concentration $p_c$, because mere connectivity does not guarantee the transmission of order even at T=0. Detailed results, including bounds on $x_c$, are presented for the three-state Potts antiferromagnet on a triangular lattice and for quadrupolar models of (o-${\mathrm{H}}_2$ ${)}_{\mathrm{x}}$(p-${\mathrm{H}}_2$ ${)}_{1\mathrm{-}\mathrm{x}}$ hydrogen mixtures on fcc and triangular lattices.