Justification of the renormalization-group method

The notion of the renormalization group (RG) in statistical physics which was introduced first in the works by Kadanoff and Wilson [1, 2] was initially formulated in terms of Hamiltonian. Later on, in some mathematical works the notion of RG was formulated as a natural generalisation of limit theorems of probability theory [3–5]. It is shown that a rigorous formalization of RG in terms of the Hamiltonian of Gibbs field is possible in the high temperature region. It is proved that RG transforms the Gibbs state into Gibbs one and the Hamiltonians of the transformed Gibbs field are calculated explicitly.