The energy density in the planar Ising model
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 obtai...
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| Veröffentlicht in: | Acta mathematica 2013-12, Vol.211 (2), p.191-225 |
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| container_title | Acta mathematica |
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| creator | Hongler, Clément Smirnov, Stanislav |
| description | 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. |
| doi_str_mv | 10.1007/s11511-013-0102-1 |
| format | Article |
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| fulltext | fulltext |
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| ispartof | Acta mathematica, 2013-12, Vol.211 (2), p.191-225 |
| issn | 0001-5962 1871-2509 |
| language | eng |
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| source | International Press Journals; SpringerNature Journals; Project Euclid Open Access; EZB-FREE-00999 freely available EZB journals |
| subjects | Boundary conditions Boundary value problems Correlation analysis Energy Energy density Free boundaries Geometry Ising model Lattices Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Phase transitions Studies |
| title | The energy density in the planar Ising model |
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