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

No abstract