Relationship among Exactly Soluble Models of Critical Phenomena. I : 2D Ising Model, Dimer Problem and the Generalized XY-Model
スポンサーリンク
概要
- 論文の詳細を見る
By relating a transfer matrix associated with a classical system to the Hamiltonian of its corresponding quantum mechanical system, it is proved that the two-dimensional Ising model in the absence of a magnetic field is equivalent to the ground state of the linear XY-model in the presence of a magnetic field, under appropriate relations among coupling parameters appearing in the two Hamiltonians. Simple relations are established for spin correlations in both systems. Consequently, the Ising system and the ground state of the XY-model are shown to exhibit similar singularities with respect to temperature and a magnetic field, respectively. It is also proved that the two-dimensional dimer problem is equivalent to the ground state of a generalized XY-model, which is solved exactly in general.
- 理論物理学刊行会の論文
- 1971-11-25
著者
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Suzuki Masuo
The Institute For Solid State Physics The University Of Tokyo
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Suzuki Masuo
The Institute Of Solid State Physics University Of Tokyo
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SUZUKI Masuo
The Institute of Solid State Physics, University of Tokyo
関連論文
- Critical Slowing Down in the Kinetic Ising Model
- Statistical Mechanics of the Finite Ising Model with Higher Spin
- Relationship among Exactly Soluble Models of Critical Phenomena. I : 2D Ising Model, Dimer Problem and the Generalized XY-Model
- Singularity of Nonlinear Response near the Critical Field. I : Static Case
- Long-Range Order in Ideal Ferromagnets
- Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism