We reveal the critical percolation in the early stage of phase transition dynamics with spontaneous Z₂-symmetry breaking in a two-dimensional continuum of non-conserved system. The percolation property is investigated numerically by mapping the real scalar field of the order parameter onto a discretized space of a square lattice and labeling the connected cluster of the lattice sites with the same sign of the field. We show that the time t_P, at which the system accomplishes the critical percolation, obeys a power law t_P∝ L^z_P of the system size L with the exponent z_P ≈ 1 distinct from the previous results in the Ising systems [1-3]. This power law behavior is obtained heuristically by counting the number of the intersection points of domain walls. The situation changes if we impose a physical rule that domain walls cannot get crossed or bifurcated in two dimensional continuum systems by taking account of the existence of the intersection points. The scaling behavior vanishes with t_P=0 and the critical percolation happens from the initial state.

[1] Thibault Blanchard, Federico Corberi, Leticia F. Cugliandolo and Marco Picco, EPL 106 (2014) 66001

[2] Thibault Blanchard, Leticia F. Cugliandolo, Marco Picco, and Alessandro Tartaglia, J. Stat. Mech. (2017) 113201.

[3] Alessandro Tartaglia, Leticia F. Cugliandolo,and Marco Picco, J. Stat. Mech. (2018) 083202.