Dimer–Dimer Correlations at the Rough–Smooth Boundary
| العنوان: | Dimer–Dimer Correlations at the Rough–Smooth Boundary |
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| المؤلفون: | Johansson, Kurt, 1960, Mason, Scott |
| المصدر: | Communications in Mathematical Physics. 400(2):1255-1315 |
| الوصف: | Three phases of macroscopic domains have been seen for large but finite periodic dimer models; these are known as the frozen, rough and smooth phases. The transition region between the frozen and rough region has received a lot of attention for the last twenty years and recently work has been underway to understand the rough–smooth transition region in the case of the two-periodic Aztec diamond. We compute uniform asymptotics for dimer–dimer correlations of the two-periodic Aztec diamond when the dimers lie in the rough–smooth transition region. These asymptotics rely on a formula found in Chhita and Johansson (Adv Math 294:37–149, 2016) for the inverse Kasteleyn matrix, they also apply to the infinite square grid dimer model with a variable weighting which interpolates between the rough and smooth phase (Kenyon et al. Ann Math (2) 163(3):1019–1056, 2006). In particular, we find that distant dimers initially decay exponentially when the magnetic coordinates are very close to the bounded complementary component of the associated amoebae, they then transition to a power law decay once far enough apart. |
| وصف الملف: | |
| URL الوصول: | https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-332156 https://doi.org/10.1007/s00220-023-04649-1 |
| قاعدة البيانات: | SwePub |
| تدمد: | 00103616 14320916 |
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| DOI: | 10.1007/s00220-023-04649-1 |