Coordination number in triangular lattice

[norman86]

Hi. I have a question on configuration numbers of graphs in lattices, often used in high dimension expansion of Ising model. A 2 point graph in a hypercubic d-dimensional lattice of N sites has a configuration number Nd, a square in the same lattice has Nd(d-1)/2. My question is: which is the configuration number of a 2 point graph and of a triangle graph in a triangular d-dimensional lattice? More generally, how are these numbers calculated? Is there any table where one can find them? Thanks in advance.

 

[BigJDubs]

The configuration number of a two point graph and a triangle graph in a triangular d-dimensional lattice can be calculated using the same formula used for a square in a hypercubic d-dimensional lattice. The formula is Nd(d-1)/2, where N is the number of sites in the lattice. Thus, the configuration number of a two point graph in a triangular d-dimensional lattice is Nd(d-1)/2, and the configuration number of a triangle graph in a triangular d-dimensional lattice is also Nd(d-1)/2. There is no specific table where you can find the configuration numbers of all graphs in different types of lattices; however, the formula given above can be applied to any type of lattice to calculate the configuration number.