Equilibrium Stranski-Krastanow and Volmer-Weber modelsD. B. Abraham1 and C. M. Newman2
1 Rudolph Peierls Centre of Theoretical Physics, University of Oxford - Oxford OX13NP, UK, EU
2 Courant Institute of Mathematical Sciences, New York University - New York, NY 10012, USA
received 11 December 2008; accepted in final form 11 March 2009; published April 2009
published online 16 April 2009
An equilibrium random surface model in 3d is defined which includes versions of both the Stranski-Krastanow and Volmer-Weber models of crystal surface morphology. In a limiting case, the model reduces to one studied previously in a different context for which exact results are available in part of the phase diagram, including the critical temperature, the associated specific heat singularity and the geometrical character of the transition. Through a connection to the 2d Ising model, there is a natural association with the Schramm-Loewner evolution that has also been observed experimentally in a nonequilibrium deposition setting.
68.43.Hn - Structure of assemblies of adsorbates (two- and three-dimensional clustering).
68.35.Rh - Phase transitions and critical phenomena.
64.60.De - Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.).
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