Exponential decay for the near-critical scaling limit of the planar Ising model

Federico Camia Division of Science, NYU Abu Dhabi, Saadiyat Island, Abu Dhabi, UAE Jianping Jiang NYU-ECNU Institute of Mathematical, Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062 P.R. CHINA Charles M. Newman Courant Institute, 251 Mercer St, New York, NY, 10012 USA

Mathematical Physics Probability mathscidoc:2203.22001

Communications on Pure And Applied Mathematics, 73, (7), 1371-1405, 2020.7
We consider the Ising model at its critical temperature with external magnetic field ha15/8 on the square lattice with lattice spacing a. We show that the truncated two-point function in this model decays exponentially with a rate independent of a as a ↓ 0. As a consequence, we show exponential decay in the near-critical scaling limit Euclidean magnetization field. For the lattice model with a = 1, the mass (inverse correlation length) is of order h8/15 as h ↓ 0; for the Euclidean field, it equals exactly Ch8/15 for some C. Although there has been much progress in the study of critical scaling limits, results on near-critical models are far fewer due to the lack of conformal invariance away from the critical point. Our arguments combine lattice and continuum FK representations, including coupled conformal loop and measure ensembles, showing that such ensembles can be useful even in the study of near-critical scaling limits. Thus we provide the first substantial application of measure ensembles.
No keywords uploaded!
[ Download ] [ 2022-03-17 15:37:18 uploaded by admin ] [ 81 downloads ] [ 0 comments ]
@inproceedings{federico2020exponential,
  title={Exponential decay for the near-critical scaling limit of the planar Ising model},
  author={Federico Camia, Jianping Jiang, and Charles M. Newman},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317153718130156993},
  booktitle={Communications on Pure And Applied Mathematics},
  volume={73},
  number={7},
  pages={1371-1405},
  year={2020},
}
Federico Camia, Jianping Jiang, and Charles M. Newman. Exponential decay for the near-critical scaling limit of the planar Ising model. 2020. Vol. 73. In Communications on Pure And Applied Mathematics. pp.1371-1405. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317153718130156993.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved