Critical temperature estimates for higher-spin Ising and Potts models

We present estimates of the critical temperature of both higher-spin Ising and Potts models on the square and simple cubic lattices based on a Husimi tree, dynamical systems approach. For the square lattice, exact results are available for the Potts model but we can refine and improve some previous estimates based on series expansions for the higher-spin Ising model. For the simple cubic lattice, based on the systematics of this approach, we are able to present accurate estimates for the critical temperature of spin systems with spin values, where estimates by other methods are unavailable or much less accurate. The same is true for the Potts model. All our estimates can be obtained using a personal computer.