On the double random current nesting field [article]

Hugo Duminil-Copin, Marcin Lis
2019 arXiv   pre-print
We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph. We also construct a nesting field for the double random current, which, under this map, corresponds to the height function of the dimer model. As applications, we provide an
more » ... ve derivation of some of the bozonization rules obtained recently by Dub\'edat, and show that the spontaneous magnetization of the Ising model on a planar biperiodic graph vanishes at criticality.
arXiv:1712.02305v2 fatcat:kj56amp6nvg4zbxrli7oplgkpy