Phase transitions in discrete low-dimensional classical models (Ising, Potts) with power-law decaying interactions are approached by two complementary methods. Renormalisation procedure based on transfer matrix, analogous to finite size scaling, which involves scaling of the interaction-range is used to study, within direct space, the second order-phase transitions in these models. Different critical regimes are covered. MC simulations are used to examine the onset of the first order phase transitions. The scaling analysis of the interface free energy, 4'th order cumulants and other quantities derived from the energy, order-parameter and cluster-size distributions is performed in order to study the change of character of the transition.

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