Critical dynamics of classical systems under slow quench

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While a large number of studies have focused on the nonequilibrium dynamics of a system when it is quenched instantaneously from a disordered phase to an ordered phase, such dynamics have been relatively less explored when the quench occurs at a finite rate. Here, we study the slow quench dynamics in two paradigmatic models of classical statistical mechanics, a one-dimensional kinetic Ising model and a mean-field zero-range process, when the system is annealed slowly to the critical point. Starting from the time evolution equations for the spin–spin correlation function in the Ising model and the mass distribution in the zero-range process, we derive the Kibble–Zurek scaling laws. We then test a recent proposal that critical coarsening, which is ignored in the Kibble–Zurek argument, plays a role in the nonequilibrium dynamics close to the critical point. We find that the defect density in the Ising model and a scaled mass distribution in the zero-range process decay linearly to their respective values at the critical point with the time remaining until the end of the quench provided the final quench point is approached sufficiently fast, and sublinearly otherwise. As the linear scaling for the approach to the critical point also holds when a system following an instantaneous quench is allowed to coarsen for a finite time interval, we conclude that critical coarsening captures the scaling behavior in the vicinity of the critical point if the annealing is not too slow.

Section: Discussionmentioning

confidence: 80%

Section: Zero-range Process In Mean-field Geometrymentioning

confidence: 99%

Slow quench dynamics in classical systems: kinetic Ising model and zero-range process

Priyanka¹,

Chatterjee²,

Jain³

2021

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“…where ν /(1 + νz c ) ≈ 0.315. This, however, is not correct in coarsening systems as already discussed in [38,39,42,43], for example.…”

Section: The Kibble -Zurek Mechanismmentioning

confidence: 93%

“…In the present study, we only consider the dynamics above T c (ie t ∈ [0, τ Q ]). Studies of the cooling rate effects on the coarsening dynamics that is at work close and below the critical point, even after annealing, have been presented in [38] for the 2d Ising model, in [39] for the 2d xy model, in [42] for a one-dimensional non-equilibrium lattice gas model with a phase transition between a fluid phase with homogeneously distributed particles and a jammed phase with a macroscopic hole cluster, and in [43,44] for time-dependent dissipative and stochastic Gross -Pitaievskii models relevant to describe micro-cavity polaritons and cold boson gases.…”

Section: Quench To T = T Cmentioning

confidence: 99%

See 1 more Smart Citation

Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model

Ricateau¹,

Cugliandolo²,

Picco³

2018

We study, with numerical methods, the fractal properties of the domain walls found in slow quenches of the kinetic Ising model to its critical temperature. We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble -Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium. arXiv:1709.05268v1 [cond-mat.stat-mech] 15 Sep 2017Since the interfaces on short length scales are not smooth anymore, their fractal dimension is given bywhere κ c = 3 is the same universal parameter as in the pre-factor in front of the logarithmic growth of the wav. Note that D c/z c ≈ 0.634 > 1 /2. The wav still has a universal behaviour, now highlighted

Coarsening and percolation in the kinetic 2d Ising model with spin exchange updates and the voter model

Tartaglia¹,

Cugliandolo²,

Picco³

2018

We study the early time dynamics of bimodal spin systems on 2d lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same model with globally conserved order parameter (nonlocal spin exchanges), and the voter model. As already observed for non-conserved order parameter dynamics (Glauber dynamics), in all the cases in which the stochastic dynamics satisfy detailed balance, the critical percolation state persists over a long period of time before usual coarsening of domains takes over and eventually takes the system to equilibrium. By studying the geometrical and statistical properties of time-evolving spin clusters we are able to identify a characteristic length p (t), different from the usual length d (t) ∼ t 1/z d that describes the late time coarsening, that is involved in all scaling relations in the approach to the critical percolation regime. We find that this characteristic length depends on the particular microscopic dynamics and the lattice geometry. In the case of the voter model, we observe that the system briefly passes through a critical percolation state, to later approach a dynamical regime in which the scaling behaviour of the geometrical properties of the ordered domains can be ascribed to a different criticality.arXiv:1805.05775v2 [cond-mat.stat-mech]