49 research outputs found
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 .Comment: 22 pages. Further details on extensions. To appear in J.Math.Phys.,
special issue on `Probabilistic Methods in Statistical Physics', March 200
On the Structure of the Set of Gibbs States for the 2-dimensional Ising Ferromagnet (Random Systems and Dynamical Systems)
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