On the equivalence of finite size scaling renormalization group and phenomenological renormalization

It is shown that the recently proposed finite size scaling renormalization group, when using systems infinite in one dimension and finite in the others, is equivalent to the Nightingale (correlation length) phenomenological renormalization. The equivalence, however, is concerned only with the critical coupling and thermal critical exponent; the finite size scaling renormalization group approach provides other exponents in a more precise and elegant fashion through the flux diagram of the recursion relations in the space spanned by the parameters of the Hamiltonian. In addition, a new set of magnetic exponents, which are so accurate as the thermal ones, can now be obtained in an easier way.