  A new graphical method is developed to calculate the critical temperature of
2- and 3-dimensional Ising models as well as that of the 2-dimensional Potts
models. This method is based on the transfer matrix method and using the
limited lattice for the calculation. The reduced internal energy per site has
been accurately calculated for different 2-D Ising and Potts models using
different size-limited lattices. All calculated energies intersect at a single
point when plotted versus the reduced temperature. The reduced temperature at
the intersection is 0.4407, 0.2746, and 0.6585 for the square, triangular, and
honeycombs Ising lattices and 1.0050, 0.6309, and 1.4848 for the square,
triangular, and honeycombs Potts lattices, respectively. These values are
exactly the same as the critical temperatures reported in the literature,
except for the honeycomb Potts lattice. For the two-dimensional Ising model, we
have shown that the existence of such an intersection point is due to the
duality relation. The method is then extended to the simple cubic Ising model,
in which the intersection point is found to be dependent on the lattice sizes.
We have found a linear relation between the lattice size and the intersection
point. This relation is used to obtain the critical temperature of the
unlimited simple cubic lattice. The obtained result, 0.221(2), is in a good
agreement with the accurate value of 0.22165 reported by others.
