Percolation in a kinetic opinion exchange model

TL;DR

This paper investigates the percolation transition of opinion clusters in a kinetic opinion exchange model, revealing a unique universality class with robust critical exponents unaffected by model parameters.

Contribution

It introduces a percolation analysis of opinion clusters in the LCCC model, identifying a distinct universality class with parameter-independent critical exponents.

Findings

Percolation transition point varies with opinion threshold.

Critical exponents are universal and independent of conviction and influence parameters.

Exponents differ from known percolation and Ising models.

Abstract

We study the percolation transition of the geometrical clusters in the square lattice LCCC model (a kinetic opinion exchange model introduced by Lallouache et al. in Phys. Rev. E 82 056112 (2010)) with the change in conviction and influencing parameter. The cluster comprises of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion (\Omega). The transition point is different from that obtained for the transition of the order parameter (average opinion value) found by Lallouache et al. Although the transition point varies with the change in the threshold value of the opinion, the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size, cluster size distribution and Binder cumulant remain same. The exponents are also independent of the values of conviction and influencing parameters indicating the robustness of this transition. The exponents do not match with that of any other known percolation exponents (e.g. the static Ising, dynamic Ising, standard percolation) and thus characterizes the LCCC model to belong to a separate universality class.