AN ORDERED PHASE WITH SLOW DECAY OF CORRELATIONS IN CONTINUUM 1/R2 ISING-MODELS

• 成果类型: Article
• 署名作者: FONTES, LRG
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989123
• 发表日期: 1993
• 页码: 1394-1412
• 关键词: percolation models; potts models; Discontinuity

摘要

For continuum 1/r2 Ising models, we prove that the critical value of the long range coupling constant (inverse temperature), above which an ordered phase occurs (for strong short range cutoff), is exactly 1. This leads to a proof of the existence of an ordered phase with slow decay of correlations. Our arguments involve comparisons between continuum and discrete Ising models, including (quenched and annealed) site diluted models, which may be of independent interest.