1School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601 2School of Physics and Material Science, Anhui University, Hefei 230601 3Department of Physics, Anqing Normal University, Anqing 246011
Abstract:We investigate the phase transitions behavior of the majority-vote model with noise on a topology that consists of two coupled random networks. A parameter p is used to measure the degree of modularity, defined as the ratio of intermodular to intramodular connectivity. For the networks of strong modularity (small p), as the level of noise f increases, the system undergoes successively two transitions at two distinct critical noises, fc1 and fc2. The first transition is a discontinuous jump from a coexistence state of parallel and antiparallel order to a state that only parallel order survives, and the second one is continuous that separates the ordered state from a disordered state. As the network modularity worsens, fc1 becomes smaller and fc2 does not change, such that the antiparallel ordered state will vanish if p is larger than a critical value of pc. We propose a mean-field theory to explain the simulation results.