TY  - JOUR
AU  - Kachapova, Farida 
AU  - Kachapov, Ilias 
PY  - 2016
TI  - Convergence of Renormalization Group Transformations of Gibbs Random Field
JF  - Journal of Mathematics and Statistics
VL  - 12
IS  - 3
DO  - 10.3844/jmssp.2016.135.151
UR  - https://thescipub.com/abstract/jmssp.2016.135.151
AB  - 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 a lattice model with weak interaction and we use semi-invariants to prove that random fields transformed by renormalization group converge 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 weakly dependent fields on a lattice.