The Pinning of a Domain Wall by Weakened Bonds in Two Dimensions

  • J. T. Chalker
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 77)


The effect of thermal fluctuations on an interface between two co-existing phases can be understood as an example of the Hohenberg, Mermin and Wagner theorem [1]. The interface between a liquid and its vapour, in the absence of a stabilising force such as gravity, provides an instance of a two-dimensional system with a continuous symmetry, under translations Vertically’. There is therefore no long-range order in the interfacial position; the interface is roughened by capillary waves, which are the relevant Goldstone modes. These considerations do not apply to a domain wall in the three-dimensional Ising model since the presence of a lattice renders the translational symmetry discrete. In this case it has been proven [2] that below the critical temperature of a corresponding two-dimensional Ising system the interface is localised near the ground-state position, whilst a range of evidence (low temperature series expansion [3], computer simulation [4] and mappings to other models [5]) suggests that just above this temperature, and well below the bulk critical point, the interface has a roughening transition to a diffuse phase dominated by capillary waves.


Domain Wall Ising Model Weakened Bond Translational Symmetry Capillary Wave 


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Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • J. T. Chalker
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of OxfordOxfordEngland

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