Crystal Statistics of a Two-Dimensional Triangular Ising Lattice

An example of a two-dimensional crystal in which each lattice point interacts with six neighbors is the so-called "triangular Ising lattice." The unit cell is a parallelogram with interactions along each of the sides and along the shorter diagonal. The thermodynamic properties of this lattice can be calculated for arbitrary interaction constants in the three independent directions by a simple extension of the procedure used previously by the author to solve the two-dimensional rectangular Ising lattice.The triangular lattice generally has an order-disorder transition of a type very similar to that of the rectangular lattice, which is indeed but a limiting case of the triangular problem. The only lattice having no transition is that for which one or three of the three interactions are antiferromagnetic (negative) and the two interaction constants of smallest absolute magnitude have equal absolute value.