Freezing in random graph ferromagnets.
Using T=0 Monte Carlo and simulated annealing simulation, we study the energy relaxation of ferromagnetic Ising and Potts models on random graphs. In addition to the expected exponential decay to a zero energy ground state, a range of connectivities for which there is power law relaxation and freezing to a metastable state is found. For some connectivities this freezing persists even using simulated annealing to find the ground state. The freezing is caused by dynamic frustration in the graphs, and is a feature of the local search nature of the Monte Carlo dynamics used. The implications of the freezing on agent-based complex system models are briefly considered.
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Institute for Theoretical Physics, Chalmers University of Technology and Göteborg University, SE-412 96 Gothenburg, Sweden. tfkps@fy.chalmers.se