Three-dimensional Antiferromagnetic Heisenberg Model Research Articles

Влияние магнитного поля на фазовые переходы в модели Гейзенберга на треугольной решетке

The Monte Carlo method was used to study phase transitions, magnetic and thermodynamic properties of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice in a magnetic field. The studies were carried out in the range of variation of the magnetic field value 0≤h≤12. The magnetic structures of the ground state are obtained in a wide range of magnetic field values. The character of phase transitions is determined on the basis of the histogram method of data analysis. It was found that in the range 0≤h≤10, a first-order phase transition is realized. It is shown that a further increase in the magnetic field value removes the degeneracy of the ground state and smears out the phase transition.

Phase diagram of the antiferromagnetic Heisenberg model on a bcc lattice with competing first and second neighbor interactions

The Monte Carlo replica algorithm was used to study the phase transitions and critical phenomena of the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with first J1 and second J2 neighbor interactions. A phase diagram for the dependence of the critical temperature (TN) on the ratio of the second neighbor interaction r=J2∕J1 was constructed. The (2/3 <r≤ 0.75) region was found in the diagram where a first order transition from the Néel phase to the paramagnetic phase occurs, whereas the phase transition from the Néel phase to collinear phase at r = 2/3, kBT∕J1=0.670(1) has a second order nature.

Исследование фазовых переходов и критических свойств модели Гейзенберга на объемно-центрированной кубической решетке

The phase transitions and critical phenomena of the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with next and next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. Investigations are carried out for relations of exchange interaction values of next and next-nearest neighbors in the range of k values [0.0, 0.6]. A behavior of phase transitions is analyzed by the histogram method. A whole set of main static critical exponents is estimated within the finite-size scaling theory. The universality class of the model critical behavior is shown to be unchanged in the considered interval of k value.

Компьютерное моделирование фазовых переходов антиферромагнитной модели Гейзенберга

Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. The phase transitions of this model are studied. The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors $r = J_2 / J_1$ in the range $0.0 \leq r \leq 1.0$. The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.

Phase Transitions in the Antiferromagnetic Heisenberg Model on a Body-Centered Cubic Lattice with Allowance for the Next-Nearest-Neighbor Interactions

Based on the replica exchange Monte Carlo algorithm and histogram analysis of data, the phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with allowance for the next-nearest-neighbor interaction are studied. The study is performed for the nextnearest- neighbor exchange interaction ratio of r = 1. It is established that, for this model, the transition from the antiferromagnetic to paramagnetic phase is a first-order phase transition.

Фазовые переходы в атиферромагнитной модели Гейзенберга на объемно-центрированной кубической решетке с учетом взаимодействий следующих ближайших соседей

AbstractBased on the replica exchange Monte Carlo algorithm and histogram analysis of data, the phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with allowance for the next-nearest-neighbor interaction are studied. The study is performed for the nextnearest- neighbor exchange interaction ratio of r = 1. It is established that, for this model, the transition from the antiferromagnetic to paramagnetic phase is a first-order phase transition.

Phase Transitions in the Antiferromagnetic Heisenberg Model on a Triangular Lattice with the Next-Nearest Neighbor Interactions

The critical behavior and phase transitions (PT) of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with nearest-neighbor (J) and next-to-nearest neighbor (J1) interactions is studied by the replica Monte Carlo method. The first order phase transition has been revealed in the studied model based on the histogram method of processing data of the Monte Carlo for systems with large linear dimensions. Shown that the system exhibits the pseudouniversal critical behavior in the case of small lattices.

Critical properties of a frustrated Heisenberg model on a stacked triangular lattice with allowance for second-nearest neighbor interaction

The critical properties of the three-dimensional antiferromagnetic Heisenberg model are investigated using the Monte Carlo method with allowance for second-nearest neighbor interaction. Pseudo-universal critical behavior of this model is observed for small lattices. A complete set of the main static magnetic and chiral indices is calculated with the use of finite-dimensional scaling theory.

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J1) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J1/J| = 0–0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.

Phase transitions in the antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions

Phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions have been studied by the histogram Monte Carlo method. Phase transitions in this model have been studied in the range of the next-nearest neighbor interactions from 0.0 to 1.0. The first-order phase transition has been revealed in the considered interval in the studied model.

SU(2) Lattice Gauge Theory Formulation of the (2+1)-Dimensional Antiferromagnetic Heisenberg Model11The project supported in part by National Natural Science Foundation of China

The equivalence of 2+1 antiferromagnetic Heisenberg model and the SU(2) Kogut Susskind lattice gauge theory is recapitulated and the naive Euclidean lattice action of the three-dimensional antiferromagnetic Heisenberg model is derived. The three-dimensional lattice gauge fermion theory is formulated to give the consistent lattice gauge theory of antiferromagnetic Heisenberg model. In continuum limit the two copies of two flavor fermions are resulted, which give the negative results of the microscopic derivation of the Chern-Simons terms. The Chern-Simons terms, the gauge invariant problem of effective action and the “chirality” are discussed.