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On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature (1406.1206v2)
Published 4 Jun 2014 in math.PR, math-ph, and math.MP
Abstract: We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\Lambda$, this probability turns out to behave like $\exp(-\tau_\beta(0) L \log L )$, with $\tau_\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.