Geometric properties of spin models

Geometric properties of spin models

  • Date: Dec 3, 2020
  • Time: 16:00 - 17:00
  • Speaker: Amanda Azevedo
  • Location: virtual platform
  • Host: Arne Traulsen
  • Contact: traulsen@evolbio.mpg.de

Many systems in nature are constantly evolving over time. In some cases, such as glassy systems, there is no clear understanding of the mechanisms underlying the microscopic dynamics that lead to the approach to an asymptotic or equilibrium state. In contrast to phenomena in equilibrium, out-of-equilibrium behavior is much less comprehended. For example, consider the problem of phase-ordering kinetics, e.g., when a system is suddenly quenched from a disordered phase to an ordered one. After the quench, ordered regions begin to form and grow via domain coarsening. When measured in units of a characteristic length scale (dynamical scaling), the domain structure is statistically the same at all times. The domain structure’s morphology holds information about the system’s geometric properties and grasps information about its phase transition. Examples of systems that exhibit this phase ordering vary from magnetic domain growth in ferromagnetic materials to the spatial segregation in bacterial populations.
Our approach to studying the geometrical properties is to measure how heterogeneously sized the equilibrium domains in a given distribution are (see [1] and references therein). This quantity, H, measures the average number of distinct domain sizes present in a given configuration. This work generalizes this observable to non-equilibrium conditions and follows it through the temporal evolution of spin systems. Its application in the 2d Ising model was able to unveil the rich interplay between percolation and coarsening dynamics. The results of H(t) indicate that this is a useful quantity to detect and separate different time scales [2].

[1] de la Rocha, A. R., de Oliveira, P. M. C. and Arenzon, J. J., Phys. Rev. E, 91, 042113 (2015).
[2] de Azevedo-Lopes, A., de la Rocha, A. R., de Oliveira, P. M. C. and Arenzon, J. J., Phys. Rev. E , 101, 012108 (2020).

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