Distribution of Zeros of the Partition Function of the Ising Model
スポンサーリンク
概要
- 論文の詳細を見る
To study the relations between Yang-Lee's theory of the phase transitions and the distribution of the partition functions in the antiferromagnetic case, the partition functions of finite (4×4 and 4×6) Ising model with the nearest and the next nearest neighbor interactions are calculated. The distributions of the zeros in the fugacity z plane of the partition function for various combinations of the values of J/kT-J'/kT or tank (J/2kT)-tanh(J'/2kT) are investigated. The patterns of the distribution of the zeros show several types corresponding to ferromagnetic state, antiferromagnetic state and superantiferromagnetic state. In the antiferromagnetic ordered state the locus of the zeros is found to be nearly two concentric circles and to cross the positive real axis at two points z_c and 1/z_c when the next neighbor ferromagnetic interaction is introduced. This means that our system shows the phase transitions at finite critical fields H_c and -H_c. The locus of zeros of Fisher's model of super-exchange antiferromgnet is also shown to cross the positive real axis at z_c and 1/z_c below the Neel temperature.
- 社団法人日本物理学会の論文
- 1971-02-05
著者
-
Abe Yoshihiko
Department Of Applied Physics Tohoku University
-
Abe Yoshihiko
Department Of Physics Tohoku University
-
YAMAMOTO MASAMI
Department of Hospital Pathology, Hiroshima University Hospital
-
Katsura Shigetoshi
Department Of Applied Physics Faculty Of Engineering Tohoku University
-
Yamamoto Masami
Department Of Applied Physics Tohoku University
関連論文
- Effects of Electrode Geometry on Breakdown Voltage of a Single-Gap Pseudospark Discharge
- Effects of Electrode Geometry and Gas Pressure on Breakdown Voltage of a Pseudospark Discharge
- Liver Cancer in Atomic-bomb Survivors: Histological Characteristics and Relationships to Radiation and Hepatitis B and C Viruses
- VISUALIZATION OF BOVINE SPERM SEX CHROMOSOMES IN PENETRATED ZONA-FREE HAMSTER OVA
- Nonlinear Susceptibility in the Spin Glass
- Renal Adaptation of Ammonia-producing Enzymes for NH_4Cl-induced Acidosis
- Tetradics Formulation of the Two-Time Green's Function Method and Its Application to the Heisenberg Ferromagnet
- Ground State and the Magnetization Process of the Body-Centered Tetragonal Lattice with Ising Spins
- The Ground State of the Ising Model of the Simple Cubic Lattice with First, Second and Third Neighbor Interactions
- Ground States of the Ising Model of the Linear Chain of S=1 with J_1 and J_2 and of S=1 / 2 with J_1, J_2 and J_3
- First Order Green Function Theory of Ferromagnetism
- Magnetic Phase Diagram for the Triangular Ising Lattice
- Phase Transitions and Distributions of Zeros of the Partition Functions for an Antiferromagnetic Ising Model and for a Hard Core Lattice Gas
- Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole
- Distribution of Zeros of the Partition Function for the Slater Model of Ferroelectricity
- Asymptotic Form of the Lattice Green's Function of the Simple Cubic Lattice
- Point of Condensation and the Volume Dependency of the Cluster Integrals
- Distribution of Zeros of the Partition Function of the Ising Model
- Critical Field of the Heisenberg Model at Zero Temperature
- Susceptibility and Specific Heat in the Glass-Like Phase : Cumulant Expansion to the Random Bond Ising Model
- Theory of Spin Glass by the Method of the Distribution Function of an Effective Field
- XY-Nature of the Fully Frustrated Ising Model on the Triangular Lattice
- Possibility of the Kosterlitz-Thouless Phase Transition in the Two Dimensional Fully Frustrated Ising Model
- Monte Carlo Simulation of the Antiferromagnetic Ising Model on the Triangular Lattice with the First and Second Neighbour Interactions
- Distribution of Zeros of the Partition Function in the Complex Temperature Plane. II
- Bethe Lattice and the Bethe Approximation
- Some Remarke on the Condensation Phenomena.
- Distribution of Roots of the Partition Function in the Complex Temperature Plane
- Asymptotic Form of the Lattice Green's Function of the Square Lattice in the Diagonal Direction
- Phase Transition of Husimi-Temperley Model of Imperfect Gas
- On the Bose-Einstein Condensation
- Cluster Sums and Related Coefficients of the Ising Model
- Annealed Ising Bond-Mixture on the Pyrite Lattices
- Diffraction of Electromagnetic Waves by Ribbon and Slit. I
- Random Mixture of the Ising Magnets in a Magnetic Field : Quenched Site and Bond Problems
- A Method of Determining the Orderings of the Ising Model with Several Neighbor Interactions under the Magnetic Field and Applications to Hexagonal Lattices