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In this article, we present a Monte Carlo study of phase transition andcoarsening dynamics in the non-conserved two-dimensional random-bond $q$-stateclock 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 differentphases when quenched from a disordered initial configuration representing atinfinite temperature. Our investigation of the equilibrium phase transitionaffirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transitiontemperatures decrease with bond randomness strength $\epsilon$. Effect of$\epsilon$ on the non-equilibrium coarsening dynamics is investigated followingindependent 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 andstructure factor are independent of $\epsilon$ and the presence of quencheddisorder slows down domain coarsening. Coarsening dynamics in both LRO and QLROregimes are further characterized by power-law growth with disorder-dependentexponents within our simulation time scales. The growth exponents in the LROregime decreases from 0.5 in the pure case to 0.22 in the maximum disorderedcase, whereas the corresponding change in the QLRO regime happens from 0.45 to0.38. We further explored the coarsening dynamics in the bond-diluted clockmodel and in both the models, the effect of the disorder is more significantfor the quench in the LRO regime compared to the QLRO regime.

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