@article {10.3844/jmssp.2016.135.151,
article_type = {journal},
title = {Convergence of Renormalization Group Transformations of Gibbs Random Field},
author = {Kachapova, Farida and Kachapov, Ilias},
volume = {12},
year = {2016},
month = {Jul},
pages = {135-151},
doi = {10.3844/jmssp.2016.135.151},
url = {https://thescipub.com/abstract/jmssp.2016.135.151},
abstract = {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.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}