Random loops, dimers, spins and the Bose gas

Taggi Lorenzo, Sapienza Università di Roma

We introduce a general random walk loop soup which reduces to or is related to several models of interest, including the Spin O(N) model, the Bose gas, the dimer model, the double dimer model, random lattice permutations. The main questions involve the characterisation of the size and the geometry of the loops. We will give an overview on these models, present some recent results about existence of macroscopic loops in three and higher dimensions [1, 2, 3] and on the absence of macroscopic loops in two dimensions [4], and state some open questions.

Area: CS28 - Statistical mechanics and interacting particle systems (Elisabetta Candellero)

Keywords: random matchings, spin systems, dimer model, random loops, interacting random walks, Bose gas

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