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We investigate a kinetic Ising model with several single-spin flip dynamics(including Metropolis and heat-bath) on quenched and annealed random regulargraphs. As expected, on the quenched structures all proposed algorithmsreproduce the same results since the conditions for the detailed balance andthe Boltzmann distribution in an equilibrium are satisfied. However, on theannealed graphs situation is far less clear -- the network annealing disturbsthe equilibrium moving the system away from it. Consequently, distinct dynamicslead to different steady states. We show that some algorithms are moreresistant to the annealed disorder, which causes only small quantitativechanges in the model behavior. On the other hand, there are dynamics for whichthe influence of annealing on the system is significant, and qualitativechanges arise like switching the type of phase transition from continuous todiscontinuous one. We try to identify features of the proposed dynamics whichare responsible for the above phenomenon.

Kinetic Ising models with various single-spin flip dynamics on quenched and annealed random regular graphs