Ground state of the antiferromagnetic Ising model of general spinSon a triangular lattice

We have investigated the ground state of the antiferromagnetic Ising model of spin S on the triangular lattice. We show that long-range order exists in the system of infinite spin. This is completely different from the case for the system of S=1/2, in which there is no long-range order. We also find that long-range order exists if S is larger than a critical value ${\mathit{S}}_{\mathit{c}}$. An upper bound on ${\mathit{S}}_{\mathit{c}}$ is obtained by the use of Peierls’ argument. The spin-correlation function 〈${\mathit{S}}_{\mathit{i}}$ ${\mathit{S}}_{\mathit{j}}$〉 behaves as (${\mathit{r}}_{\mathit{i}\mathit{j}}$ ${)}^{\mathrm{-}\mathrm{\eta }}$, where η=0 for S>${\mathit{S}}_{\mathit{c}}$, while η=1/2 for S=1/2 (Stephenson). We have calculated η for various spin values with the Monte Carlo method. Thus it is shown that the spin magnitude is an important physical parameter in our frustration system.