Ground state of the antiferromagnetic Ising model of general spin<i>S</i>on a triangular lattice

Abstract

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{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, where \ensuremath{\eta}=0 for S&gt;${\mathit{S}}_{\mathit{c}}$, while \ensuremath{\eta}=1/2 for S=1/2 (Stephenson). We have calculated \ensuremath{\eta} 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.