Percolation and number of phases in the 2D Ising model

We reconsider the percolation approach of Russo, Aizenman and Higuchi for showing that there exist only two phases in the Ising model on the square lattice. We give a fairly short alternative proof which is only based on FKG monotonicity and avoids the use of GKS-type inequalities originally needed for some background results. Our proof extends to the Ising model on other planar lattices such as the triangular and honeycomb lattice. We can also treat the Ising antiferromagnet in an external field and the hard-core lattice gas model on $Z^2$.Comment: 22 pages. Further details on extensions. To appear in J.Math.Phys., special issue on `Probabilistic Methods in Statistical Physics', March 200

ニジゲンイジングモデルノキョクゲンギブスブンプニツイテ

京都大学0048新制・課程博士理学博士甲第1936号理博第478号新制||理||261(附属図書館)5497UT51-52-N1京都大学大学院理学研究科数学専攻(主査)教授 渡辺 信三, 教授 吉沢 尚明, 教授 伊藤 清学位規則第5条第1項該当Kyoto UniversityDA