A Note on Exponential Decay in the Random Field Ising Model |
| |
Authors: | Federico Camia Jianping Jiang Charles M Newman |
| |
Institution: | 1.Division of Science,NYU Abu Dhabi,Abu Dhabi,United Arab Emirates;2.Department of Mathematics,VU University Amsterdam,Amsterdam,The Netherlands;3.NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai,Shanghai,China;4.Courant Institute of Mathematical Sciences,New York University,New York,USA |
| |
Abstract: | For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|