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Modelo de Heisenberg com campo aleatório e interação Dzyaloshinskii-Moriya

Joeliton Barros da Silva

Published Dec 20, 2018• 0 citations
OpenAlex

Abstract

The critical behavior of systems that exhibit magnetism has been the subject of intense research. The Heisenberg model deserves special attention because it is a tool to be used to describe the properties of many magnetic, insulators and anisotropic materials. In addition, it is known that the consideration of anisotropic effects in many spin models can result in the presence of tricritical behavior in the phase diagram and thermodynamic properties. In particular, the Dzyaloshinskii-Moriya (DM) interaction consists of an important type of anisotropy, which since the last decades has attracted a great deal of attention, playing an important role in the description of some classes of insulators, as well as in the study of the phenomena involving spin-glass, among others. The presence of disorder in the models, introduced by random variables governed by a given probability distribution, also usually results in the alteration of the critical behavior in relation to the homogeneous system. Therefore, the interest in the systems in the presence of random field has grown. With such motivation, the spin-1/2 and spin-1 anisotropic Heisenberg models with DM interaction and magnetic random field are studied within the framework of Oguchi’s pair approximation. Although the approach is developed for lattices with general coordination number z the model is discussed in detail for the simple cubic lattice (z = 6). The critical behavior dependent on both the DM parameter and the random field is analyzed. The investigation of phase diagrams reveals the presence of tricritical points and the results are extended to describe the behavior of the thermodynamic properties of the system.

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The critical behavior of systems that exhibit magnetism has been the subject of intense research. The Heisenberg model deserves special attention because it is a tool to be used to describe the properties of many magnetic, insulators and anisotropic materials. In addition, it is known that the consideration of anisotropic effects in many spin models can result in the presence of tricritical behavior in the phase diagram and thermodynamic properties. In particular, the Dzyaloshinskii-Moriya (DM) interaction consists of an important type of anisotropy, which since the last decades has attracted a great deal of attention, playing an important role in the description of some classes of insulators, as well as in the study of the phenomena involving spin-glass, among others. The presence of disorder in the models, introduced by random variables governed by a given probability distribution, also usually results in the alteration of the critical behavior in relation to the homogeneous system. Therefore, the interest in the systems in the presence of random field has grown. With such motivation, the spin-1/2 and spin-1 anisotropic Heisenberg models with DM interaction and magnetic random field are studied within the framework of Oguchi’s pair approximation. Although the approach is developed for lattices with general coordination number z the model is discussed in detail for the simple cubic lattice (z = 6). The critical behavior dependent on both the DM parameter and the random field is analyzed. The investigation of phase diagrams reveals the presence of tricritical points and the results are extended to describe the behavior of the thermodynamic properties of the system.
We have employed the Oguchi approximation (OA) to investigate the effects of a random crystal field which is active (inactive) with probability [Formula: see text] [Formula: see text] for given lattice sites on the thermodynamic properties of the mixed spin-[Formula: see text] anisotropic Heisenberg model in the presence of an external magnetic field. By exploiting the thermal variations of the order parameters, interesting phase diagrams are produced on various planes. The phase diagrams show first- and second-order transition lines and also tricritical points. In addition to the reentrant behavior which is localized in a certain range of [Formula: see text] at very low temperature, the magnetic exponent [Formula: see text] calculated near the critical point exhibits interesting behaviors depending on the crystal field interaction. The hysteresis behavior of the model is also investigated and it reveals that the width of hysteresis loop decreases or increases, respectively, for negative or positive crystal field region as the probability [Formula: see text] increases.
We have studied the critical properties of the three-dimensional random anisotropy Heisenberg model by means of numerical simulations using the Parallel Tempering method. We have simulated the model with two different disorder distributions, cubic and isotropic ones, with two different anisotropy strengths for each disorder class. For the case of the anisotropic disorder, we have found evidence of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder. In the case of isotropic disorder distribution the situation is very involved: we have found two phase transitions in the magnetization channel which are merging for larger lattices remaining a zero magnetization low-temperature phase. Studying this region using a spin-glass order parameter we have found evidence for a spin-glass phase transition. We have estimated effective critical exponents for the spin-glass phase transition for the different values of the strength of the isotropic disorder, discussing the crossover regime.
The random field Ising model (RFIM) has been investigated extensively both theoretically and experimentally in recent years [1–4]. Some questions, such as the lower critical dimension and the existence of a static phase transition, have already been solved from the theoretical point of view, but other questions, such as the existence of the tricritical point, are still open. However, it is now understood that the RFIM describes the essential physics of a rich class of experimentally accessible disordered systems. These include structural phase transitions in random alloys, commensurate charge-density-wave systems with impurity pinning, binary fluid mixtures in random porous media, and the melting of intercalates in layered compounds such as TiS2. The behavior of the RFIM is governed by the competing tendencies of the spins to align ferromagnetically under impetus of the exchange or to follow the local fields and thus be uncorrelated. The RFIM has been studied using different methods. One of the authors [5] of the present paper has developed a new version of effective field theory, which extends the approximation methods [6, 7] to random Ising systems, in which randomness can be described by discrete random variables and the geometry of the lattice can be easily taken into account. This method is based on the determination of the probability distribution of the discrete variables, which takes into account exactly the self-site correlations. This approach has been used to study cooperative phenomena and phase transitions in various systems, and gives useful qualitative and quantitative insights for the critical behavior of a wide variety of classical and quantum lattice spin systems [8–10]. In recent decades, the renormalization group theory of phase transitions and critical phenomena represents one of the most powerful tools of theoretical physics. Therefore, employing this theory (which can be applied for weak fields), the proof
In this work we investigate the Blume-Capel (BC) model with infinite-range interactions in a Gaussian random magnetic field . The model can be solved exactly and exhibits rich phase diagrams, obtained from analytical and numerical study of the free energy density. Initially we review the BC model solution under the influuence of a uniform crystalline anisotropy field and zero magnetic feld recovering results well known in the literature. Then we review the BC model under the effect of a random magnetic field with bimodal distribution and uniform crystal field as introduced by Kaufman and Kanner, giving special attention to phase diagrams in terms of anisotropy versus temperature. Finally, we performed a study of the model in random magnetic field obeying a Gaussian distribution.The chosen phase diagrams exhibit very rich behavior in terms of critical phenomena including in some cases tricritical points, associated with lines of first-order transitions and continuous transitions.
This thesis presents renormalization group (RG) analyses of two strongly correlated condensed matter systems. In the first part, the phase diagram of the spin-12\frac{1}{2}21​ Heisenberg antiferromagnetic model on a spatially anisotropic triangular lattice is discussed. This model, together with a Dzyaloshinskii-Moriya (DM) interaction, describes the magnetic properties of the layered Mott insulator Cs2_{2}2​CuCl4_{4}4​. Employing a real-space RG approach, it is found, in agreement with a previous similar study, that a fragile collinear antiferromagnetic (CAF) state can be stabilized at sufficiently strong anisotropies. The presented RG analysis only indicates the presence of the CAF and spiral states in the phase diagram, with no extended quantum-disordered state at strong anisotropies. Specifically, it reveals a fine-tuning of couplings that entails the persistence of ferromagnetic correlations between second-nearest chains over large length scales even in the CAF phase. This has important implications on how numerical studies on finite-size systems should be interpreted, and reconciles the presence of the CAF state with the observation of only ferromagnetic correlations in numerical studies. The effect of a weak DM interaction within this RG approach is examined. It is concluded that Cs2_{2}2​CuCl4_{4}4​ is well within the stability region of the spiral ordering. In the second part, the fate of a neck-narrowing Lifshitz transition in two-dimensions and in the presence of weak interactions is studied. Such a transition is a topological quantum phase transition, with no change in symmetry. At the critical point of this transition, the density of states at the Fermi energy is logarithmically divergent and a van Hove singularity appears. It is found that, at the critical point, the Wilsonian effective action is intrinsically non-local. This non-locality is attributed to integrating out an emergent soft degree of freedom. Away from the critical point, a local perturbative RG description is presented, and it is shown that weak attractive interactions grow as log⁡2L\log^2Llog2L (LLL is the physical length). However, this local description is restricted to a finite momentum range that shrinks as the critical point is approached.