The energy density in the planar Ising model

• 成果类型: Article
• 署名作者: Hongler, Clement; Smirnov, Stanislav
• 署名单位: Columbia University; University of Geneva; Saint Petersburg State University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0102-1
• 发表日期: 2013
• 页码: 191-225
• 关键词: conformal-invariance; crystal statistics

摘要

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.