TRIANGULAR ANTI-FERROMAGNETIC ISING-MODEL WITH A TRANSVERSE FIELD AT ZERO TEMPERATURE

The ground-state properties of the triangular antiferromagnetic Ising model with Ising constant J in a transverse field h are investigated by a real-space renormalisation group method. For h=0, the known properties (energy=-J, finite entropy, no order) are recovered. For h not=0, the ground state remains highly degenerate, no order exists and the correlation function exhibits power-law behaviour up to (h/J)c approximately=1.41, where a phase transition takes place to a non-degenerate ground state. At h/J=(h/J)c, power-law behaviour is still observed for the correlation function but with a different exponent. Just above this region a gap Delta opens ( Delta approximately ((h/J)-(h/J)c)s with s=0.8) and the coherence length of the correlation function xi diverges as xi varies as ((h/J)-(h/J)c)-v with v=0.8. This corresponds to a three-dimensional classical model where h is replaced by the temperature. In this type of system, where the ground state has a degeneracy proportional to N2/3 it is predicted that a transition will occur at a finite T c to a low-temperature phase without order but with power-law behaviour for the correlation function, as for the classical XY model in two dimensions.