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We present the results of the Monte-Carlo simulation of graphene-likestatistical model in terms of occupation numbers. We study the problem of thephase transition in graphene to an insulating phase. Only antiferromagneticorder parameter was studied at the moment by means of Hybrid Monte-Carloprocess on the hexagonal lattice because of the sign problem for excitonicorder parameter in fermionic determinant. Therefore we have studied thepossibility of the phase transition to an excitonic phase by means ofsimplified Monte-Carlo process on the hexagonal lattice. We show that thisphase, which corresponds to a charge polarization of graphene sublattices, canappear at some values of Coulomb electron-electron potentials. In this work westudy the dependence of the phase transition characteristics on the strength ofon-site electron-electron interaction. We show that excitonic phase transitionis also impossible in suspended graphene.

Monte-Carlo simulation of graphene in terms of occupation numbers for the excitonic order parameter at hexagonal lattice