Block-diagonalizable two-dimensional generalized Ising systems (BD2DGIS): the free energy

The paper is a continuation of arXiv:2012.10364, where the approach was developed to constructing the exact matrix model for any generalized Ising system, and such model was constructed for certain 2d system. In this paper, the properties of the model are specified for light block diagonalization. A corresponding example is considered. For the example, general exact partition function is obtained and analysed. The analysis shows that the free energy does not depend on the amount of rows with a large amount of cells. For the example with light boundary conditions, the partition function is obtained and the specific free energy per spin is plotted.