Phase transition of two-dimensional Ising model on random point patterns.

The phase transition of two-dimensional Ising model on random point patterns is investigated using Monte Carlo simulation and the critical temperature is calculated using the Bethe approximation. We find a linear relation between the critical temperature and the structural characteristics of the random point pattern, as described by Aboav's parameter. Numerical results and analytical calculation both yield this linear relation with a similar slope, though the intercept is different due to the Bethe approximation.