Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

Ordering kinetics in a q-state random-bond clock model: Role of vortices and interfaces

In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the nonconserved two-dimensional random-bond q-state clock model (RBCM) deriving from a pure clock model [Chatterjee et al., Phys. Rev. E 98, 032109 (2018)10.1103/PhysRevE.98.032109]. 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 ε. Effect of ε on the nonequilibrium 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 is independent of ε 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 timescales. The growth exponents in the LRO regime decrease 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.

Ordering kinetics in a q-state random-bond clock model: Role of vortices and interfaces

In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the nonconserved two-dimensional random-bond q-state clock model (RBCM) deriving from a pure clock model [Chatterjee et al., Phys. Rev. E 98, 032109 (2018)10.1103/PhysRevE.98.032109]. 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 ε. Effect of ε on the nonequilibrium 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 is independent of ε 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 timescales. The growth exponents in the LRO regime decrease 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.

Coarsening dynamics in the Vicsek model of active matter

We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as [Formula: see text] (with [Formula: see text] , while the velocity length scale grows much faster, viz., [Formula: see text] (with [Formula: see text] . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively.

Random field Ising model in a uniform magnetic field: Ground states, pinned clusters and scaling laws

In this paper, we study the random field Ising model (RFIM) in an external magnetic field h . A computationally efficient graph-cut method is used to study ground state (GS) morphologies in this system for three different disorder types: Gaussian, uniform and bimodal. We obtain the critical properties of this system and find that they are independent of the disorder type. We also study GS morphologies via pinned-cluster distributions, which are scale-free at criticality. The spin-spin correlation functions (and structure factors) are characterized by a roughness exponent [Formula: see text]. The corresponding scaling function is universal for all disorder types and independent of h.

Columnar domains and anisotropic growth laws in dipolar systems

Magnetic and dielectric solids are well-represented by the Ising model with dipolar interactions (IM+DI). The latter are long-ranged, fluctuating in sign, and anisotropic. Equilibrium studies have revealed novel consequences of these complicated interactions, but their effect on nonequilibrium behavior is not explored. We perform a deep temperature quench to study the kinetics of domain growth in the d=3 IM+DI. Our main observations are (i) the emergence of columnar domains along the z axis (Ising axis) with a transient periodicity in the xy plane; (ii) anisotropic growth laws: ℓ_{ρ}(t)∼t^{ϕ}; ℓ_{z}(t)∼t^{ψ}, where ρ[over ⃗]=(x,y) and ℓ is the characteristic length scale; (iii) generalized dynamical scaling for the correlation function: C(ρ,z;t)=g(ρ/ℓ_{ρ},z/ℓ_{z}); and (iv) an asymptotic Porod tail in the corresponding structure factor: S(k_{ρ},0;t)∼k_{ρ}^{-3}; S(0,k_{z};t)∼k_{z}^{-2}. Our results explain the experimentally observed columnar morphologies in a wide range of dipolar systems, and they have important technological implications.