Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet

Abstract

We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations.

30 pages, 4 figures, submitted to J.Phys.A

References in corpus (15)

• Critical phenomena in complex networks
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Critical behavior of Griffiths ferromagnets
• Parallel dynamics of disordered Ising spin systems on finitely connected random graphs
• Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network
• Finitely connected vector spin systems with random matrix interactions
• Analytic solution of attractor neural networks on scale-free graphs
• Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
• Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
• Spin models on random graphs with controlled topologies beyond degree constraints
• Dynamical replica analysis of processes on finitely connected random graphs I: vertex covering
• A Monte Carlo Algorithm for Sampling Rare Events: Application to a Search for the Griffiths Singularity
• Statics and dynamics of the Lebwohl-Lasher model in the Bethe approximation
• Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet
• Dynamics of an Ising Spin Glass on the Bethe Lattice

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