Papers by Keyword: Frustration

Abstract: We studied magnetic orderings and frustrations on 1D chain and 2D lattices: square, triangular, kagome, and hexagonal in the Ising, 3-state Potts and standard 4-state Potts models. The spins interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or the third-neighbor exchange interactions and by an external magnetic field. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for maximum eigenvalue of Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is related to the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the topology of a lattice.

Abstract: We investigated the Ising model on a linear chain with arbitrary spin including interactions between nearest and next-nearest neighbors in an applied magnetic field. A series of exact solutions and formulas for frustration fields, magnetizations and entropies at these fields at T→0 are found.

Abstract: It has been found that the temperature dependences of the Young’s modulus for rare-earth cobaltites RBaCo₄O₇ (R = Dy - Er, Y) exhibit significant hysteresis and irreversible effects over a wide range (80–280) K between the structural and magnetic phase transition temperatures. At the magnetic phase transition temperature, there are weak and smoothed anomalies of the Young’s modulus, which correlate with the low dimensionality and frustration of the exchange interactions in the Kagome lattice of the Co subsystem for the studied rare-earth cobaltites.

Abstract: Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient D in the spin-wave spectrum E_k ~ Dk² vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of D. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.

Abstract: The phase transitions in antiferromagnetic Ising model are studied on a body-centered cubic lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transitions of second order. A static magnetic critical indices is calculated using the finite-dimensional scaling theory.

Abstract: A model for the description of two-subsystem Heisenberg ferrimagnet with frustrated intersubsystem exchange and competition between exchange interactions in a subsystem is proposed. The conditions of the existence of noncollinear Yafet-Kittel state and partially ordered magnetic structure are investigated. The phase diagram of competition parameter vs temperature is obtained in the mean field approximation. The peculiarities of the succesive magnetic phase transitions are considered.

Abstract: The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

Abstract: 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.

Abstract: Elastic properties of rare-earth cobaltites RBaCo₄O₇ (R = Y, Er - Lu) are studied in the temperature range (4.2 - 300) K. Significant softening of Youngs modulus for Lu-and Yb-cobaltites is found at temperature decrease, showing an instability of the crystal structure and accompanying by a reverse jump at the structural phase transition. Softening and jump at phase transition decrease more than by the order of value, while the transition temperature T_s and hysteresis dT_s enlarge from Lu-to Tm-and Er-compounds. Smooth and weak elastic anomaly at the magnetic phase transition is found resulting from low dimension and frustration of exchange interactions in the Co subsystem in most of the rare-earth cobaltites studied.

Abstract: We study the critical behavior of three-dimensional antiferromagnet Heisenberg model with nearest-neighbor (J) and next-nearest-neighbor (J₁) interactions by the Monte Carlo method using a high-effective replica exchange algorithm. Here is calculated a full set of main static critical exponents for values R =J₁/J= 0.0; 0.025; 0.05; 0.075; 0.1; 0.115 using the finite-size scaling theory. A phase diagram of dependency of the critical temperature on a relation between nearest-neighbor and next-nearest-neighbor R is plotted.