TY - JOUR
T1 - Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions
AU - Gandica Lopez, Yerali Carolina
AU - Chiacchiera, Silvia
PY - 2016/3/17
Y1 - 2016/3/17
N2 - We study F coupled q-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F=2,3. Using the Lee-Kosterlitz method, we find that it is continuous for F=2 and q=2, whereas it is abrupt for higher values of q and/or F. When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.
AB - We study F coupled q-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F=2,3. Using the Lee-Kosterlitz method, we find that it is continuous for F=2 and q=2, whereas it is abrupt for higher values of q and/or F. When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.
UR - http://www.scopus.com/inward/record.url?scp=84962258072&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.93.032132
DO - 10.1103/PhysRevE.93.032132
M3 - Article
AN - SCOPUS:84962258072
SN - 1539-3755
VL - 93
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 032132
ER -