Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network.
We study the bond percolation on a one-parameter family of a hierarchical small-world network and find the metatransition between an inverted Berezinskii-Kosterlitz-Thouless (iBKT) transition and an abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and the fractal exponent is discontinuous in the iBKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and the fractal exponent in each transition vanish as they approach the metatransition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this metatransition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation.
Faculty of Medicine, Toho University, 5-21-16, Omori-Nishi, Ota-ku, Tokyo 143-8540, Japan.
Tomoaki
T
Nogawa
Graduate School of Information Science, Tohoku University, 6-3-09, Aramaki-Aza-Aoba, Sendai, Miyagi 980-8579, Japan.
Takehisa
T
Hasegawa