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The paper is a continuation of arXiv:2012.10364, where the approach wasdeveloped to constructing the exact matrix model for any generalized Isingsystem, and such model was constructed for certain 2d system. In this paper,the properties of the model are specified for light block diagonalization. Acorresponding example is considered. For the example, general exact partitionfunction is obtained and analysed. The analysis shows that the free energy doesnot depend on the amount of rows with a large amount of cells. For the examplewith light boundary conditions, the partition function is obtained and thespecific free energy per spin is plotted.

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