TY - JOUR
T1 - Ising percolation in a three-state majority vote model
AU - Balankin, Alexander S.
AU - Martínez-Cruz, M. A.
AU - Gayosso Martínez, Felipe
AU - Mena, Baltasar
AU - Tobon, Atalo
AU - Patiño-Ortiz, Julián
AU - Patiño-Ortiz, Miguel
AU - Samayoa, Didier
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/2/5
Y1 - 2017/2/5
N2 - In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the “magnetization” of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.
AB - In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the “magnetization” of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.
KW - Critical exponents
KW - Majority vote model
KW - Non-consensus state
KW - Percolation
KW - Universality classes
UR - http://www.scopus.com/inward/record.url?scp=85007378336&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2016.12.001
DO - 10.1016/j.physleta.2016.12.001
M3 - Artículo
SN - 0375-9601
VL - 381
SP - 440
EP - 445
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 5
ER -