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Conformal Invariance of Spin Pattern Probabilities in the Planar Ising Model

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Weyl vs. conformal

Alexander Monin, Georgios Karananas

In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY li ...

Elsevier2016

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

Frédéric Mila, Natalia Chepiga

We report on a detailed investigation of the spin-1 J1−J2−J3 Heisenberg model, a frustrated model with nearest-neighbor coupling J1, next-nearest neighbor coupling J2, and a three-site interaction J3[(Si−1⋅Si)(Si⋅Si+1)+H.c.] previously studied in [Phys. Re ...

2016

Crossing Probabilities in Topological Rectangles for the Critical Planar FK-Ising model

Clément Hongler

We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundary conditions, generalizing results of [DCHN11] and [CS12]. Our result relies ...

Institute of Mathematical Statistics2016

Comment on “Frustration and multicriticality in the antiferromagnetic spin-1 chain”

Frédéric Mila, Natalia Chepiga

The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest-neighbor interactions, recently investigated by Pixley, Shashi, and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently o ...

2016

Conformal symmetry of the critical 3D Ising model inside a sphere

We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and t ...

Springer2015

Conformal Invariance of Spin Correlations in the Planar Ising Model

Clément Hongler

We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming fro ...

2015

Lattice Representations of the Virasoro Algebra I : Discrete Gaussian Free Field

Clément Hongler

Most two-dimensional massless field theories carry represe ntations of the Virasoro algebra as consequences of their conformal symmetry. Recently, conformal symmetry has been rigorously established for scaling limit s of lattice models by means of discrete ...

2015

Discrete Holomorphicity and Ising Model Operator Formalism

Clément Hongler, Ali Zahabi

We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct connection with the ...

2014

Convergence of Ising Interfaces to Schramm's SLE Curves

Clément Hongler, Stanislav Smirnov

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm’s SLE curves with parameter κ = 3 and κ = 16 / 3 respectively. ...

2014

The Energy Density in the Planar Ising Model

Clément Hongler, Stanislav Smirnov

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 discrete fermionic spinor and compute its scaling limit by discrete complex anal ...

2013