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arXiv · 2509.23120

Exponentially slow Mixing arising from Entropic Repulsion in $p$-SOS model

Seokun Choi
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Abstract

We investigate the Glauber dynamics of the generalized (2+1)-dimensional $p$-SOS model, $1 0$ depending on $p$ and $\beta$. We also give a refined metastability analysis: for every $0 0$ depends on $p$. The proof extends the Peierls-type contour estimates developed for $p=1$ to the nonlinear $p$-SOS setting. These results show that entropic repulsion induces uniformly slow mixing across the full $p$-SOS family, extending a phenomenon previously established only for $p=1$.

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Seokun Choi. 2025-09-27. Exponentially slow Mixing arising from Entropic Repulsion in $p$-SOS model. https://doi.org/10.1007/s10955-026-03661-8

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