Phase-ordering kinetics on graphs

Abstract

We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_{\chi }$ for the integrated response function, at variance with all the other exponents, is independent on temperature and on the presence of pinning. This universal character suggests a strict relation between $a_{\chi }$ and the topological properties of the networks, in analogy to what observed on regular lattices.

16 pages, 35 figures

References in corpus (3)

• Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
• Generic features of the fluctuation dissipation relation in coarsening systems
• Aging dynamics and the topology of inhomogenous networks

Cited by in corpus (26)

• Exact mean first-passage time on the T-graph
• Nonlinear response and fluctuation dissipation relations
• Fluctuation-Dissipation relations far from Equilibrium
• Fluctuation-dissipation relations and field-free algorithms for the computation of response functions
• Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Coarsening in inhomogeneous systems
• Scaling in the Aging Dynamics of the Site-diluted Ising Model
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses
• Fluctuations and effective temperatures in coarsening
• Phase ordering in disordered and inhomogeneous systems
• Topological regulation of activation barriers on fractal substrates
• Fractal character of the phase ordering kinetics of a diluted ferromagnet
• Phase ordering and universality for continuous symmetry models on graphs
• Fluctuations of two-time quantities and non-linear response functions
• Phase ordering in 3d disordered systems
• Non-equilibrium critical properties of the Ising model on product graphs
• Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter
• Growth Kinetics and Aging Phenomena in a Frustrated System
• Coarsening and percolation in the Ising Model with quenched disorder
• Metric characterization of cluster dynamics on the Sierpinski gasket
• Critical dynamics of long range models on Dynamical Lévy Lattices
• Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration
• Effects of Frustration on Fluctuation-dissipation Relations
• Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures