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Coarsening and percolation in 2d kinetic Ising models, and quench dynamics of the isolated p=2 spherical spin glass model

Abstract : This thesis is divided into two independent parts. In the first part, we study the early time dynamics of some 2d kinetic Ising models subject to an istantaneous quench from the disordered to the ordered phase. The post-quench relaxation dynamics is realised by means of stochastic spin update rules, of various types, which are simulated numerically through Monte Carlo methods. Measurements of different observables related to the statistical and geometrical properties of ordered domains suggest that the relaxation dynamics approaches a dynamical scaling regime with features ascribed to 2d critical percolation. In all the cases in which the stochastic dynamics satisfies detailed balance, the critical percolation state persists over a very long period of time before usual coarsening of domains takes over and leads the system to equilibrium. In the second part, we study the Hamiltonian dynamics of the 2-spin spherical spin glass model, following a uniform quench of the strength of the disorder. In each case, we consider initial conditions from Gibbs-Boltzmann equilibrium at a given temperature, and subsequently evolve the configurations with Newton dynamics dictated by a new Hamiltonian, obtained from the initial one by a uniform quench of the interaction couplings. We notice that the post-quench dynamics of this model is equivalent to that of the Neumann integrable model, and thus we analyse the integrals of motion, using them to show that the system is not able to reach an equilibrium stationary state à la Gibbs-Boltzmann.
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Alessandro Tartaglia. Coarsening and percolation in 2d kinetic Ising models, and quench dynamics of the isolated p=2 spherical spin glass model. Condensed Matter [cond-mat]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS365⟩. ⟨tel-02865361⟩

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