Abstract.
We study the phase transition in the honeycomb dimer model (equivalently, monotone non-intersecting lattice path model). At the critical point the system has a strong long-range dependence; in particular, periodic boundary conditions give rise to a “resonance” phenomenon, where the partition function and other properties of the system depend sensitively on the shape of the domain.
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The research leading to this article was conducted in part while the first author was visiting Microsoft.
Mathematics Subject Classification (2000): 82B20
Revised version: 7 July 2003
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Kenyon, R., Wilson, D. Critical resonance in the non-intersecting lattice path model. Probab. Theory Relat. Fields 130, 289–318 (2004). https://doi.org/10.1007/s00440-003-0293-z
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DOI: https://doi.org/10.1007/s00440-003-0293-z
Keywords
- Boundary Condition
- Phase Transition
- Partition Function
- Periodic Boundary
- Periodic Boundary Condition
Applied Scientific Research 6, 240–244 (1957)
Applied Scientific Research 6, 225–239 (1957)