Virtual walks and phase transitions in the two-dimensional Biswas-Chatterjee-Sen model with extreme switches

In kinetic exchange models of opinion formation, one considers pairwise interactions to update the states of the agents. We have studied a kinetic exchange model with three opinion states $0,\pm 1$, by considering a walk in a one-dimensional virtual space which evolves according to the dynamical states of the agents. The model involves two noise parameters $p$ and $q$; $p$ represents the fraction of negative interactions and $q$ corresponds to the probability of a stronger interaction with the other agent, which may result in extreme switches (change of state from $+1$ to $-1$ or vice versa). The nature of the walks can indicate where the phase transitions occur in the $p\text{−}q$ plane; these results are corroborated with those obtained using finite-size scaling method. The criticality is found to be Ising-like, even when extreme switches are allowed. A new critical exponent associated with the probability distribution of the displacements in the virtual space is also obtained independent of the values of the critical parameters. The nature of the walks is compared to similar virtual walks studied earlier.