  By means of numerical simulations, we explore possible effects of a special
interparticle interaction potential which is a function of external and
internal conditions of graphene-like systems. In addition to the
electromagnetic interaction, we introduce a new potential due to the exchange
of a massive scalar, associated to the so-called Kekul\'e deformations; this
interaction displays a spin-dependent profile. It turns out that the magnitude
of Kekul\'e deformation may significantly affect physical properties of
graphene. A Monte Carlo analysis enables one to analyze the behavior of the
system under variation of the applied external field, temperature, and the
particular type of the exchanged excitation that induces the potential. We
pursue an investigation of the spin configurations, we analyze differences in
thermal equilibrium magnetization and we carry out calculations of the magnetic
susceptibility and the specific heat in the presence of the Kekul\'e-induced
new potential.
