Topological regulation of activation barriers on fractal substrates

Abstract

We study phase-ordering dynamics of a ferromagnetic system with a scalar order-parameter on fractal graphs. We propose a scaling approach, inspired by renormalization group ideas, where a crossover between distinct dynamical behaviors is induced by the presence of a length $\lambda$ associated to the topological properties of the graph. The transition between the early and the asymptotic stage is observed when the typical size $L(t)$ of the growing ordered domains reaches the crossover length $\lambda$. We consider two classes of inhomogeneous substrates, with different activated processes, where the effects of the free energy barriers can be analytically controlled during the evolution. On finitely ramified graphs the free energy barriers encountered by domains walls grow logarithmically with $L(t)$ while they increase as a power-law on all the other structures. This produces different asymptotic growth laws (power-laws vs logarithmic) and different dependence of the crossover length $\lambda$ on the model parameters. Our theoretical picture agrees very well with extensive numerical simulations.

13 pages, 4 figures

References in corpus (12)

• Determining mean first-passage time on a class of treelike regular fractals
• Nonlinear response and fluctuation dissipation relations
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Ageing in disordered magnets and local scale-invariance
• Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
• Superuniversality in phase-ordering disordered ferromagnets
• Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
• Aging in coarsening diluted ferromagnets
• Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model
• Geometric properties of two-dimensional coarsening with weak disorder
• Aging dynamics and the topology of inhomogenous networks
• Phase ordering and universality for continuous symmetry models on graphs

Cited by in corpus (3)

• Coarsening in inhomogeneous systems
• Phase ordering in disordered and inhomogeneous systems
• Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration