High temperature series expansions of the susceptibility and second moment of the 1 / 2 , 1, 2 and infinite spin Ising models on a triangular lattice are obtained and the spin dependence of the critical indices gamma and nu investigated.
The high-temperature susceptibility of the spin-S Ising model on the triangular net is analyzed as a function of S using tenth-order high-temperature series expansions. In particular the spin dependence of the critical temperature and the amplitude of the dominant singularity are obtained by assuming a universal value $\ensuremath{\gamma}=\frac{7}{4}$ for the critical exponent of the susceptibility. The results, for the critical temperature particularly, provide a valuable guidepost in judging the convergence of recent nonlinear renormalization-group calculations for these models.
Reports studies of the critical behaviour of the Ising model with first and second neighbour interactions J 1 , J 2 on the triangular lattice. High-temperature series have been used to determine the locations of the ferromagnetic critical line and the critical line in the region (J 1 <0, J 2 >0). On the latter line the ordering susceptibility appears to diverge algebraically with the exponent gamma approximately 2.4. The existence of a sinusoidal phase and an associated Lifshitz point are conjectured.
Extended series expansions for the high temperature zero-field susceptibility of the Ising model are given in powers of the usual high temperature counting variable v=tanh K; for the triangular lattice to v 16 , for the square lattice to v 21 and for the honeycomb lattice to v 32 , inclusive. The asymptotic behaviour of the ferromagnetic and antiferromagnetic susceptibility is studied. It is concluded that the ferromagnetic singularity is not exactly factorizible. The antiferromagnetic susceptibility of the square and honeycomb lattices has a singularity of the same type as the energy at the antiferromagnetic critical temperature.
The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for the general d-dimensional (hyper)simple-cubical lattices. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general d expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of 1/d.