Coarsening and percolation in the Ising Model with quenched disorder

F Insalata , F Corberi , F Cugliandolo (1) , M. Picco (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

Through large-scale numerical simulations, we study the phase ordering kinetics of the 2d Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities-the winding angle and the pair-connectedness-we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model. 1. Introduction Phase ordering kinetics, the ordering of a system via domain growth after a quench from the homogeneous phase into one with broken symmetry, has attracted great interest in the last 50 years [1]. A simple example is a ferromagnet, instantaneously cooled (quenched) from above to below the critical point. The initial equilibrium state becomes unstable after the quench and evolves towards one of the two possible symmetry-related ordered configurations with opposite magnetizations. Relaxation toward the new equilibrium state occurs slowly (i.e. not exponentially fast) by the formation and growth (coarsening) of domains of the two equilibrium phases (i.e. group of aligned spins). This domain growth is driven by superficial tension, i.e. the interfaces tend to become flatter due to energetic reasons. Over time, the smallest domains disappear so that the typical size R(t) of the remaining ones increases. One theoretical approach to this class of problem is the kinetic Ising Model (IM), originally introduced by Glauber [2]. One starts with a Ising system in which each spins is randomly oriented, a situation that can be described as equilibrium at infinite temperature, T → ∞. Then, the evolution of the system is treated as a Markov chain, with appropriate transition probabilities. The dynamical evolution can be simulated through standard Monte Carlo methods [3]. In the thermodynamic limit, the coarsening process goes on indefinitely, with none of the two equilibrium phases (up and down spins in this case) prevailing at any given finite time. This means that the magnetic system does not develop a magnetization, or equivalently that on average up spins are in the same number as down spins.

Domains: Other [cond-mat.other]; Physics [physics]

F Insalata, F Corberi, F Cugliandolo, M. Picco. Coarsening and percolation in the Ising Model with quenched disorder. Journal of Physics: Conference Series, 2018, 956, pp.012018. ⟨10.1088/1742-6596/956/1/012018⟩. ⟨hal-01982529⟩