The energy density in the planar Ising model

2013/01/01 by Clément Hongler, Stanislav Smirnov · 11 citations
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Quantum many-body systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.1007/s11511-013-0102-1

Abstract

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 correlator and compute its scaling limit by discrete complex analysis methods. As a consequence, we obtain a simple exact formula for the scaling limit of the energy field one-point function in terms of the hyperbolic metric. This confirms the predictions originating in physics, but also provides a higher precision.

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• Rotational invariance in critical planar lattice models
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• Conformal Invariance of the FK-Ising Model on Lorentz-Maximal S-Embeddings
• Universality of Ising spin correlations on critical doubly-periodic graphs
• Three-point connectivity constant for q-state Potts spin clusters
• Conformal Invariance of Spin Correlations in the Planar Ising Model
• Scaling limits of discrete holomorphic functions
• Massive Scaling Limit of the Ising Model: Subcritical Analysis and Isomonodromy
• Percolation and O(1) loop model
• A Generalization of Cardy's and Schramm's Formulae. [europepmc]

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