Monte Carlo studies on small Ising systems

Results are presented for the critical temperatures $T_n$ of small $n\times n$ Ising clusters using one of the extended mean-field boundary conditions recently introduced by Bolton and Johnson. The spin flips were simulated numerically. The values of $T_n$ were obtained by extrapolating to zero the long-range order below $T_n$. The extrapolation to the infinite limit $n=\infty$ was performed using an expansion in powers of $\frac{1}{n}$ and the final result agrees to 2% with the Onsager value.