Ising Chains Antiferromagnetically Coupled on a Triangular Lattice

Abstract

We have investigated models composed of infinitely many Ising magnetic chains creating a triangular or hexagonal lattice. These models with nearest-neighbor antiferromagnetic interactions are frustrated and it is known that the first one is disordered at all finite temperatures, whereas the second one undergoes a finite temperature continuous phase transition to a phase with a three-sublattice structure. The Linear Perturbation Renormalization Group is used to predict the critical temperature for the Ising chains with ferro- or antiferromagnetic intrachain interaction ( k = J / k B T ) coupled by weaker interchain interactions ( k 1 = J '/ k B T ). The inverse critical temperature k c as function of k 1 / k is found for the systems in two and three dimensions for both ferro- and antiferromgnetic interactions. For the standard ferromagnetic Ising model ( k 1 = k ) on the triangular lattice we have found k c = 0.268 which should be compared with the exact value k c = 0.274. We have also calculated the speci...