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We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher [Fis66] introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer… (More)

In this paper, we study the bead model : beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two consecutive beads on a wire, there must be exactly one bead on each neighboring wire. We construct a one-parameter family of Gibbs measures on the bead configurations that are uniform in a… (More)

We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical Z 2 , triangular and honeycomb lattice at the critical temperature. Fisher [Fis66] introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract The XOR-Ising model on a graph consists of random spin configurations on vertices of the graph obtained by taking the product at each vertex of the spins of two independent Ising models. In this paper, we explicitly relate loop configurations of the XOR-Ising model and those of a dimer model living… (More)

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for liquid and gaseous Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an… (More)

We introduce a one-parameter family of massive Laplacian operators (∆ m(k)) k∈[0,1) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for minus the inverse of ∆ m(k) , the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study… (More)

We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several fundamental combinatorial objects as special cases, such as plane partitions, tilings of Aztec diamonds, pyramid… (More)

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