Coupled order-parameter system on a scale-free network.
The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T<Tc, when O(n) symmetry is present. This behavior is related to the appearance of Goldstone modes.
Palchykov
V
V
Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine. palchykov@icmp.lviv.ua
von Ferber
C
C
Folk
R
R
Holovatch
Yu
Y