Multiple phases and vicious walkers in a wedge
We consider a statistical system in a planar wedge, for values of the bulk parameters corresponding to a first order phase transition and with boundary conditions inducing phase separation. Our previous exact field theoretical solution for the case of a single interface is extended to a class of sys...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2015-12-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321315003715 |
| Summary: | We consider a statistical system in a planar wedge, for values of the bulk parameters corresponding to a first order phase transition and with boundary conditions inducing phase separation. Our previous exact field theoretical solution for the case of a single interface is extended to a class of systems, including the Blume–Capel model as the simplest representative, allowing for the appearance of an intermediate layer of a third phase. We show that the interfaces separating the different phases behave as trajectories of vicious walkers, and determine their passage probabilities. We also show how the theory leads to a remarkable form of wedge covariance, i.e. a relation between properties in the wedge and in the half plane, which involves the appearance of self-Fourier functions. |
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| ISSN: | 0550-3213 1873-1562 |