Poissonian behavior of Ising spin systems in an external field

We apply the Stein-Chen method for Poisson approximation to spin-half Ising -type models in positive external field which satisfy the FKC inequality. I n particular, we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) var iable, the distribution of minus spins is approximately Poisson. The error of the approximation is inversely proportional to the number of lattice sit es (we obtain upper and lower bounds on the total variation distance betwee n the exact distribution and its Poisson approximation). We illustrate thes e results by application to specific models, including the mean-field and n earest neighbor ferromagnetic Ising models.