Lattice statistics on plane, cylinder and torus

In this paper the relations among entropy constants of lattice statistics on plane, cylinder and torus are discussed. We show that for many statistical models, the entropy constant of a plane lattice is the same as the entropy constants of the corresponding cylindrical and toroidal lattices. As a result, we get the entropy constants of quadratic lattices on cylinder and torus. Furthermore, we consider three more complex lattices which can not be handled by a single transfer matrix. Using the concept of transfer multiplicity we extend results of quadratic lattice to these three lattices and obtain lower and upper bounds of the entropy constants.