Phase transitions and universality in the Sznajd model with anticonformity

TL;DR

This paper investigates the phase transitions in the Sznajd opinion model with anticonformity on lattices, estimating critical exponents and suggesting it belongs to the Ising universality class.

Contribution

It provides the first numerical estimates of critical exponents for the model on lattices and compares them to the Ising universality class.

Findings

The model exhibits phase transitions with critical exponents matching the Ising universality class.

Numerical estimates of exponents $eta$, $ u$, and $ au$ were obtained for different lattice dimensions.

The results support the universality hypothesis linking the model to the Ising class.

Abstract

In this work we study the dynamics of opinion formation in the Sznajd model with anticonformity on regular lattices in two and three dimensions. The anticonformity behavior is similar to the introduction of Galam's contrarians in the population. The model was previously studied in fully-connected networks, and it was found an order-disorder transition with the order parameter exponent $\beta=1/2$ calculated analytically. However, the other phase transition exponents were not estimated, and no discussion about the possible universality of the phase transition was done. Our target in this work is to estimate numerically the other exponents $\gamma$ and $\nu$ for the fully-connected case, as well as the three exponents for the model defined in square and cubic lattices. Our results suggest that the model belongs to the Ising model universality class in the respective dimensions.