The classical one-dimensional Heisenberg magnet in an external magnetic field. Transfer matrix formalism as an application of renormalization group theory “avant la lettre”

The classical one-dimensional Heisenberg magnet is treated in the context of renormalization theory. This treatment is shown to be equivalent to the usual transfer matrix approach. If the chain consists of N spins, the original hamiltonian will, upon repeated application of the renormalization transformation, be transformed into N uncoupled spins described by N identical one-particle hamiltonians, Heff, which depends upon the original interaction and field.