Sequences of phase transitions in Ising models on correlated networks

Using the generic example of Ising spins on scale-free networks, we demonstrate that degree-degree correlations can induce a large number of thermodynamically stable states in networks that otherwise exhibit only the two completely ordered states. The additional stable states are related to the layered network structure. As one increases the temperature, a cascade of first-order phase transitions is found, at which some layers of the network become disordered, while others remain ordered. Negative degree-degree correlations are found to stabilize ordered layers against thermal fluctuations. Positively correlated networks can exhibit an infinite number of ground states and phase transitions, while in negatively correlated networks both numbers are finite.