  Statistical mechanics describes interaction between particles of a physical
system. Particle properties of the system can be modelled with a random field
on a lattice and studied at different distance scales using renormalization
group transformation. Here we consider a thermodynamic limit of Ising model
with weak interaction and we use semi-invariants to prove that a random field
transformed by renormalization group converges in distribution to an
independent field with Gaussian distribution as the distance scale infinitely
increases; it is a generalization of the central limit theorem to the Ising
model.
