The Ising magnetization exponent on is

• 成果类型: Article
• 署名作者: Camia, Federico; Garban, Christophe; Newman, Charles M.
• 署名单位: Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0526-8
• 发表日期: 2014
• 页码: 175-187
• 关键词: INEQUALITIES

摘要

We prove that for the Ising model defined on the plane at the average magnetization under an external magnetic field behaves exactly like The proof, which is surprisingly simple compared to an analogous result for percolation [i.e. that on the triangular lattice (Kesten in Commun Math Phys 109(1):109-156, 1987; Smirnov and Werner in Math Res Lett 8(5-6):729-744, 2001)] relies on the GHS inequality as well as the RSW theorem for FK percolation from Duminil-Copin et al. (Commun Pure Appl Math 64:1165-1198, 2011). The use of GHS to obtain inequalities involving critical exponents is not new; in this paper we show how it can be combined with RSW to obtain matching upper and lower bounds for the average magnetization.