Universality in the 2D Ising model and conformal invariance of fermionic observables Export

@article{citeulike:5938306, abstract = {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 invariance has ever been given, and even physics arguments support (a priori weaker) M\"obius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures.}, archivePrefix = {arXiv}, author = {Chelkak, Dmitry and Smirnov, Stanislav}, citeulike-article-id = {5938306}, citeulike-linkout-0 = {http://arxiv.org/abs/0910.2045}, citeulike-linkout-1 = {http://arxiv.org/pdf/0910.2045}, day = {11}, eprint = {0910.2045}, keywords = {2d, conformal, ising-model, sle}, month = {Oct}, posted-at = {2009-11-06 15:47:19}, priority = {2}, title = {Universality in the 2D Ising model and conformal invariance of fermionic observables}, url = {http://arxiv.org/abs/0910.2045}, year = {2009} }

TY - JOUR ID - citeulike:5938306 L3 - citeulike-article-id:5938306 N2 - 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 invariance has ever been given, and even physics arguments support (a priori weaker) M\"obius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures. TI - Universality in the 2D Ising model and conformal invariance of fermionic observables KW - 2d KW - conformal KW - ising-model KW - sle AU - Chelkak, Dmitry AU - Smirnov, Stanislav PY - 2009/Oct/11/ UR - http://arxiv.org/abs/0910.2045 ER -