# Julian Sienkiewicz from Warsaw University of Technology presented a talk titled "Cricriticality in the q-neighbor Ising model on a partially duplex clique" today

Julian Sienkiewicz, Associate Professor from the Department of Physics at Warsaw University of Technology in Warsaw, Poland, presented a talk titled "Cricriticality in the q-neighbor Ising model on a partially duplex clique". In the talk Prof. Sienkiewicz shows how a modified kinetic Ising model -- a so-called q-neighbor Ising model -- behaves on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model one is able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q = 3, discontinuous phase transition for q >= 4, and for q = 1 and q = 2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q = 1 and q = 2. Subsequently we introduce a partially duplex clique, parametrized by r in [0,1], which allows us to tune the network from monoplex (r = 0) to duplex (r = 1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r at which a tricriticality (switch from continuous to discontinuous phase transition) appears.

The talk was sponsored by the European Union Renoir project led by Prof. Janusz Holyst of Warsaw University of Technology and RPI's team of Prof. Boleslaw Szymanski is one of the U.S. partners of this project.