Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field -: art. no. 036112

The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K-nn, next-nearest-neighbor couplings K-nnn>0, and a magnetic field H. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K-nn<0, but we also explore the ferromagnetic regime K(nn)greater than or equal to0 for H=0. For K-nn<0 and H=0 we locate a critical phase presumably covering the whole range -infinity<K-nn<0. For K-nn<0, Hnot equal0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H-->infinity this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.