Theory of correlation and susceptibility based on the confluent transfer matrix and its associated transfer matrix

The correlation function and susceptibility of the Ising model on regular lattices are shown to be studied from the CAM analysis of a systematic series of hierarchical models such as generalized cactus trees by introducing a new transfer matrix associated with the confluent transfer matrix. In this method, the singularity of the correlation length can be obtained. Each systematic solution yields the exponents ν = 1, γ = 1 and η = 1.