Journal of Statistical Physics

, Volume 58, Issue 3–4, pp 685–706 | Cite as

Rigorous derivation of domain growth kinetics without conservation laws

  • Daniel Kandel
  • Eytan Domany
Articles

Abstract

The time evolution of the Ising model that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops atT=0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we show that the average lifetime of such a domain is proportional to its area. We also consider theT=0 dynamics of a single infinite quadrant. The area of the quadrant decreases during the time evolution, and we show that the area lost grows linearly with time. We solve a first passage time problem as well. That is, we calculate the average time it takes for the area lost to reach a given value for the first time. Lastly, we map the infinite quadrant model onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical six-vertex model.

Key words

Domain growth kinetics Ising model six-vertex model 

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Daniel Kandel
    • 1
  • Eytan Domany
    • 1
  1. 1.Department of ElectronicsWeizmann Institute of ScienceRehovotIsrael

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