### Speaker

Andrzej Krawiecki
(Faculty of Physics, Warsaw University of Technology)

### Description

Majority vote model on random graphs and scale-free networks is investigated, in which a
fraction p of agents (called contrarians or anticonformists)
follows an antiferromagnetic update rule, i.e., they assume, with
probability governed by a parameter q (0 < q < 1/2), the opinion opposite to that of the majority
of their neighbors, while the remaining 1-p fraction of agents follows the usual ferromagnetic update
rule assuming, with probability governed by the same parameter q, the opinion in accordance with
that of the majority of their neighbors. For p=1 it is shown by Monte Carlo simulations and using
the Binder cumulants method that for decreasing q the model undergoes second-order
phase transition from a disordered (paramagnetic) state to a spin-glass-like state,
characterized by a non-zero value of the spin-glass order parameter measuring the overlap of
agents' opinions in two replicas of the system, and simultaneously by the magnetization close to
zero. Besides, in this state the correlation of the agents' opinions exhibits exponentially
decaying oscillations, as expected in the spin-glass phase.
In the case of the model on scale-free networks the critical value of the parameter q weakly
depends on the details of the degree distribution. As p is decreased, the critical value of q
falls quickly to zero and only the disordered phase is observed. On the other hand, for p close to
zero for decreasing q the usual ferromagnetic transition is observed.

### Primary author

Andrzej Krawiecki
(Faculty of Physics, Warsaw University of Technology)