GROUND-STATE OF THE ANTIFERROMAGNETIC ISING-MODEL OF GENERAL SPIN-S ON A TRIANGULAR LATTICE

We have investigated the ground state of the antiferromagnetic Ising model of spin S on the triangular lattice. We show 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 S(c). An upper bound on S, is obtained by the use of Peierls' argument. The spin-correlation function [S(i)S(j)] behaves as (r(ij))-eta, where eta=0 for S > S(c), while eta=1/2 for S=1/2 (Stephenson). We have calculated 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.