Ordering kinetics in q-state random-bond clock model: Role of Vortices and Interfaces

Abstract

In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the non-conserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Phys. Rev. E 98, 032109 (2018)]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transition temperatures decrease with bond randomness strength $\epsilon$. Effect of $\epsilon$ on the non-equilibrium coarsening dynamics is investigated following independent rapid quenches in the quasi-long range ordered (QLRO, $T_c^2<T<T_c^1$) regime and long-range ordered (LRO, $T<T_c^2$) regime at temperature $T$. We report that the dynamical scaling of the correlation function and structure factor are independent of $\epsilon$ and the presence of quenched disorder slows down domain coarsening. Coarsening dynamics in both LRO and QLRO regimes are further characterized by power-law growth with disorder-dependent exponents within our simulation time scales. The growth exponents in the LRO regime decreases from 0.5 in the pure case to 0.22 in the maximum disordered case, whereas the corresponding change in the QLRO regime happens from 0.45 to 0.38. We further explored the coarsening dynamics in the bond-diluted clock model and in both the models, the effect of the disorder is more significant for the quench in the LRO regime compared to the QLRO regime.

References in corpus (16)

• Novel type of phase transition in a system of self-driven particles
• Aging, rejuvenation and memory : the example of spin glasses
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• A new model of binary opinion dynamics: coarsening and effect of disorder
• Non-equilibrium relaxation of an elastic string in a random potential
• Ageing in disordered magnets and local scale-invariance
• Growing correlations and aging of an elastic line in a random potential
• Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• 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
• Geometric properties of two-dimensional coarsening with weak disorder
• Kosterlitz-Thouless transition in planar spin models with bond dilution
• Approximating the XY model on a random graph with a $q$-state clock model
• Ordering Kinetics in the Random Bond XY Model

Cited by in corpus (1)

• Ordering kinetics in the active Ising model