Multiple phases and vicious walkers in a wedge

Gesualdo Delfino; Alessio Squarcini

doi:10.1016/j.nuclphysb.2015.10.019

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arXiv · 1509.00310

Multiple phases and vicious walkers in a wedge

Gesualdo Delfino·Alessio Squarcini

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Abstract

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 {\it 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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Gesualdo Delfino, Alessio Squarcini. 2015-09-01. Multiple phases and vicious walkers in a wedge. https://doi.org/10.1016/j.nuclphysb.2015.10.019

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