Modelling militantism and partisanship spread in the chain and square lattice opinion structures by using q-XY opinion model

In this work we have studied the spreading of militantism in 1D and 2D square lattice by operating the q-XY opinion and its utility optimization as control mechanism for the update process. The average utility and opinion value for a pair of opinion nodes are calculated in the framework of standard statistical mechanics using the q-opinion utility U = − J 2 ( O → 2 − 2 ) − F O → + q ( J 2 ( O → 2 − 2 ) ∗ F O → ) . The agreement with an incoming zealot opinion is modelled as one by one dialogue starting from a random opinion configuration. Each time step one node updates its opinion value according to a set of rules and by specific probabilities based on local utility improvement. New opinion values are accepted with a Metropolis-like probability calculated by employing q-utilities of the nodes under updating process. For the chain opinion structure in the interaction type preserving regimes where 0$?> 1 − q J 2 ( O → 2 − 2 ) > 0 given 0 ≤ O ≤ 1 it resulted that that both 1D and 2D structures accept the militant offer only partially. For bounded chain the agreement level is at average values for short chain and low values for bounded long opinion chain. Bounded chain structures are found resistant toward militantism accommodation. For square opinion lattices we obtained also that the militant attitude would never cover all the community. Homogenous-nodes group resulted somewhat deterring in accepting the militant opinion with an agreement level of around 0.6. For heterogonous communities the edge agreement level closed up to around 0.7-0.8. The model reproduces the fact that there would be always a fraction of opposition whatsoever regime is applied. It produces various outcomes imitating the complexity of the social behaviour.