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Journal of Physics Conference Series

Interplay of frustrations, interaction length, and dilution on magnetic transitions in vector models

Petr Dmitrievich Andriushchenko, Alexei A. Peretyatko, Vitalii Yu. Kapitan, Alexander V. Perzhu, Konstantin Valentinovich Nefedev

Published Dec 1, 2017• 2 citations
Publisher

Abstract

The research of one-dimensional Ising model with the different number of neighbors and the different sign of the exchange integral were performed. The clustered order parameter is proposed for the description of the magnetic transition in spin systems regardless of the sign of the exchange integral and the number of neighbors. The method of calculation of critical field to change the magnetic states was presented. For diluted 1D antiferromagnetic model two plateaus in magnetization behavior are observed, and explained. Influence of length of interaction plays critical role for phase transition of dipoles system. Dipoles on hexagonal lattice show the phase transition only in model of long range interaction, and there isn't critical behavior for short range. The approach to calculation of spin system in Heisenberg model is proposed.

DOI
10.1088/1742-6596/936/1/012081

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The research of one-dimensional Ising model with the different number of neighbors and the different sign of the exchange integral were performed. The clustered order parameter is proposed for the description of the magnetic transition in spin systems regardless of the sign of the exchange integral and the number of neighbors. The method of calculation of critical field to change the magnetic states was presented. For diluted 1D antiferromagnetic model two plateaus in magnetization behavior are observed, and explained. Influence of length of interaction plays critical role for phase transition of dipoles system. Dipoles on hexagonal lattice show the phase transition only in model of long range interaction, and there isn't critical behavior for short range. The approach to calculation of spin system in Heisenberg model is proposed.
The research of one-dimensional Ising model with the different number of neighbors and the different sign of the exchange integral were performed. Magnetization shows the transition from disorder to order (in finite systems) only at positive exchange integral JJJ but clustered order parameter describes the transition regardless of the sign of the exchange integral and the number of neighbors.
Critical behavior of Ising ferromagnetic systems with the competition between short- and long-range interactions near the point of a second-order phase transition has been investigated. The effects of long-range interaction lead to the need to calculate the influence of next-nearest spins, which lie inside the sphere of a specific radius. The study was carried out for a power law of decreaseing the exchange integral with distance for a three-dimensional Ising model with a cubic lattice. A comparison with the results of a field-theoretical approach and data of real experiments has been carried out. It has been shown that the critical temperature grows linearly with an increase in the parameters of long-range interaction. Critical exponents have been calculated at different parameters of long-range interaction. It is shown that at small dimensions of a system it is the short-range interaction that exerts the dominant effect on the critical behavior of the system. With an increase in the linear dimension of the system, long-range forces begin to dominate.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.
The current state of research on phase transitions and critical phenomena in frustration is considered. modeled Ising models. The results obtained on the basis of highly efficient algorithms are discussed. Monte Carlo method for Ising models on lattices of various dimensions and types. A main attention given to the results of studying phase transitions, critical and thermodynamic properties of models Ising, taking into account the exchange interactions of the first and second neighbors, as well as the external magnetic fields. Phase diagrams of the dependence of the critical temperature on the value of the exchange interactions of second neighbors and an external magnetic field. The regions of observation of phase transitions of the first and second kind. The universality classes of critical behavior are established. For some models have ranges with non-universal critical behavior. Discussed features of the critical behavior of frustrated Ising models.
The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J 1) 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 = |J 1/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.