Related papers: From the planar Ising model to quasiconformal mapp…

We discuss the notion of s-embeddings $\mathcal{S}=\mathcal{S}_\mathcal{X}$ of planar graphs carrying a nearest-neighbor Ising model. The construction of $\mathcal{S}_\mathcal{X}$ is based upon a choice of a global complex-valued solution…

We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…

We consider a class of non-integrable 2D Ising models, whose Hamiltonian, in addition to the nearest neighbor couplings, includes weak multi-spin interactions, even under spin flip. We study the model in cylindrical domains of arbitrary…

We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…

We study the spin n-point functions of the planar Ising model on a simply connected domain \Omega discretised by the square lattice \delta\mathbb{Z}^{2} under near-critical scaling limit. While the scaling limit on the full-plane \mathbb{C}…

We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a fermionic observable and compute its scaling limit by discrete…

We establish conformal invariance of Ising spin correlations on critical doubly periodic graphs, showing that their scaling limit coincides with that of the critical square lattice, as originally proved by Chelkak, Hongler and Izyurov. To…

It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal…

We prove convergence of multiple interfaces in the critical planar q = 2 random cluster model, and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple…

In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…

We construct new conserved quasi-local energies in general relativity using the formalism developed by \cite{CWY}. In particular, we use the optimal isometric embedding defined in \cite{yau,yau1} to transplant the conformal Killing fields…

We introduce Kadanoff-Ceva order-disorder operators in the quantum Ising model. This approach was first used for the classical planar Ising model and recently put back to the stage. This representation turns out to be equivalent to the loop…

We show on non-flat but critical s-embeddings the celebrated convergence of the interface curves of the critical FK Ising model to an $\operatorname{SLE}_{16/3}$ curve, using discrete complex analytic techniques first used in…

We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…

We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation…

The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation.…

First, an algebraic criterion for integrability is discussed -the so-called `superintegrability'- and some results on the classification of superintegrable quantum spin Hamiltonians based on sl(2) are obtained. Next, the massive phases of…

This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion…

In the second article of this series, we establish the convergence of the loop ensemble of interfaces in the random cluster Ising model to a conformal loop ensemble (CLE) --- thus completely describing the scaling limit of the model in…

Extensions of the Standard Model and general relativity featuring a UV fixed point can leave observable implications at accessible energies. Although mass parameters such as the Planck scale can appear through dimensional transmutation, all…