• Directed Ising type dynamic preroughening transition in one dimensional interfaces,
    Jae Dong Noh, Hyunggyu Park, and Marcel den Nijs, Phys. Rev. E, 59 , 194-204 (1999).

  • absorbing state dynamics:

    Absorbing phase transitions take place in dynamic processes with a trap, out of which the system can not escape, a non-fluctuating ground state.

    For example, in epidemic processes it is the state where everybody is healthy and the decease has died out. The epidemy propagates by direct contact. When the infection probability at contact, p, is small, the decease dies out. Beyond a critical point, the so-called percolation threshold pc, it stays alive forever and keeps recurring throughout the population (assuming the immunization period is short).

    The scaling properties at the percolation threshold are universal. They do not depend on the details of the infection process, and the context of the process, e.g., forest fires or surface catalysis.

    The typical width of the infected region l and the life time t of the decease diverge at pc as t~lz with z the dynamic exponent.

    Critical exponents like z only depend on the spatial dimension and whether there is only one single trap or two by symmetry equivalent ones. The first type of process is known as directed percolation and the latter as directed Ising.


    Dynamic rule for a one dimensional model with a dynamic disorderd flat phase
    and a Directed Ising type dynamic preroughening transition

    absorbing states in surface growth:

    The kinks in steps on a surface can be classified as up and down kinks, and be interpreted as two types of particles, A and B. In a normal step flow growth regime such kinks can be created in pairs, 0->A+B, and the step is rough.

    However the step becomes ultimately perfectly straight (the absorbing state) if we forbid 0->A+B, i.e., block deposition and evaporation of particles at flat surface segments. The only remaining processes, pair annihilation A+B->0 and kink hopping along the step, can not maintain step roughness.

    A directed Ising type transition occurs when we introduce branching of kinks, like A->ABA, near existing particles, i.e., allow particle deposition and evaporation in the direct vicinity of existing kinks. There are two topological distinct types of branching processes, as shown in the figure above.

    The DI type absorbing transition in the phase diagram represents a dynamic analogue of a preroughennig transition into a disordered flat phase.


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