Purely quadrupolar spin-1 Ising model in a transverse field

A quantum Ising-like spin-1 model characterized by quadrupolar interaction, coupled to an external anisotropic field with both dipole and quadrupole momenta is analyzed. The general phase diagram (including temperature), as well as order parameter, specific heat, and susceptibility are evaluated in the mean-field approximation and exibit a rich structure with transitions of 2° and 1° order and tricritical points. ForT=0 the phase diagram is examined also by a recently formulated improved version of mean-field theory which has the usual mean-field theory as its zero-th order approximation.     

Coupled m-component fields with cubic anisotropy

The critical behavior at phase transitions of two coupled, m-component systems with cubic anisotropy is studied by a simplified model in which the fluctuations are partially considered. The phase transition could be a new fluctuation-induced first order transition into the anisotropic phase, or a new second order phase transition. Unlike in uncoupled systems, the second order phase transition could be into either the anisotropic or isotropic phase. As expected, upon suppression of fluctuations, all results reduce to those of mean field theory.     

A mean-field theory for strongly disordered non-frustrated antiferromagnets

Motivated by impurity-induced magnetic ordering phenomena in spin-gap materials like TlCuCl₃, we develop a mean-field theory for strongly disordered antiferromagnets, designed to capture the broad distribution of coupling constants in the effective model for the impurity degrees of freedom. Based on our results, we argue that in the presence of random magnetic couplings the conventional first-order spin-flop transition of an anisotropic antiferromagnet is split into two transitions at low temperatures, associated with separate order parameters along and perpendicular to the field axis. We demonstrate the existence of either a bicritcal point or a critical endpoint in the temperature–field phase diagram, with the consequence that signatures of the spin flop are more pronounced at elevated temperature.     

Order-order and order-disorder transitions in the quantum spin-1 Ising-Heisenberg models

The critical properties of a quantum spin-1 ferromagnetic multidimensional Ising-Heisenberg model with uniaxial and single-ion anisotropy are examined in the framework of a mean-field approximation. A Landau free energy expansion is performed to identify critical lines and surfaces. The resulting phase diagram, defined in a three-dimensional space characterized by a single-ion anisotropy variable, a parameter measuring the interaction anisotropy and the temperature, is particularly interesting because it exhibits three different phases, one paramagnetic and two ferromagnetic; the latter two differing for the orientation of the dipolar ordering. The presence of both first order reorientation transitions (order-order transitions) and order-disorder transitions makes the present model promising for describing several physical systems.     

Optical studies of the ferroelastic phase transitions in KFe(MoO4)2

ABSTRACT

The ferroelastic phase transitions in KFe(MoO₄)₂ have been studied by means of polarized light microscopy. The crystal undergoes a sequence of ferroelastic phase transitions. It has been found that the second transition consists of two transitions separated by the temperature interval of about 0.4 K. Both these transitions are of the first order and are evidenced through a phase front passing, without the domain structure rebuilding. The disposition of optical indicatrix axes n_g, n_m has been established, and the birefringence has been measured in the plane (0001) in the temperature range covering all ferroelastic phases. From temperature studies of the morphic birefringence, a critical exponent of the order parameter has been estimated.     

The influence of the lithium concentration on the low-temperature phase transition in phases LixV2O5 with shcherbinaite-structure

With high-resolution Guinier diffractometry the low-temperature stability of the intercalated lithium vanadium oxide bronzes ε - Li _x V₂O₅, with 0.32 ≤ x ≤ 0.80, was studied. In the course of these investigations a line of thermally induced structural phase transitions was detected in the x-T field. The reversible continuous phase transitions can be described in terms of a classical Landau-type theory. They are proper (potentially) ferroelastic with an one-dimensional order parameter transforming as the Γ⁺ ₃ irreducible representation of space group Pmmn. The symmetry is orthorhombic P2₁/m2₁/m2/n above T_c , but monoclinic P2₁ /m11 below T_c .

The transition temperatures depend strongly on the stoichiometry of the intercalated lithium ions. The critical exponent β, and, hence, the character of the phase transition do not change significantly with the lithium concentration. However, for x ≤ 0.52 corresponding phase transitions could not be detected, supporting the idea that the accepted stability field of ε - Li _x V₂O₅(0.32 ≤ x ≤ 0.80) should be subdivided into two fields, ε- and ε'-phase, according to whether the phase transition occurs, or not. The influence of the reduction rate of the intercalated phases on the critical parameters will be discussed in terms of a mean-field theory.     

Metamagnetic model in a field of arbitrary direction

The free energy of a metamagnetic model, in a magnetic field making an angle θ with the direction of uniaxial anisotropy, is calculated in the context of the mean-field approximation. The tricritical temperature decreases as θ increases, and finally vanishes for θ larger than a certain critical angle. In the (H_∥, H_⊥, T) space there is a line of tricritical points which separates two smoothly joining surfaces of first and of second order phase transitions.     

Critical behaviour of elastically coupled systems with spatially anisotropic critical fluctuations

The spatial anisotropy of critical fluctuations has strong influence on the temperature dependence of the elastic constants of an elastic medium coupled magneto- or electrostrictive to the order parameter. Under pinned boundary conditions we find for uniaxial dipolar systems of hexagonal and trigonal symmetry a second order phase transition, where only c₁₁ and c₁₂ show critical behaviour. For other symmetries a first order transition is expected. At an uniaxial Lifshitz point only c₃₃ becomes critical and the phase transition remains of second order for any symmetry.     

The kinetic spin-1 Blume-Capel model with Glauber dynamic

We study the dynamic phase transitions (DPT), within a mean-field approach, in the kinetic spin-1 Blume-Capel model by using the Glauber-type stochastic dynamics. The nature of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameter and the Lyapunov exponent. The phase diagram is constructed in the temperatures (T) and single-ion anisotropy amplitude (D) plane. Our results predict first-order transitions at low temperature and large anisotropy strengths, which correspond in the phase diagram to the existence of a nonequilibrium tricritical point (TCP). We compare our results with the equilibrium phase diagram.     

Symmetry reduction in the phase transitions of alkali cyanides

For the Landau type phase transitions of alkali cyanides the symmetry of the order parameter and general relevant structural changes including orientational distribution of the CN molecules have been found. All phase transitions are driven by the representation of either the elastic dipol or the elastic quadrupol of the CN molecule and this leads to either ordered or disordered head-tail distribution at CN molecules. It is shown that the monoclinic phaseAa would be the result of condensation of at least two irreducible representations ofFm3m space group and that the CN molecules in this phase can be still disordered with respect to head-tail orientation.     

Dynamic transitions in Domany-Kinzel cellular automata on small-world network

We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p.     

Dynamic phase transitions and the effects of frequency of oscillating magnetic field on the dynamic phase diagrams in the bilayer honeycomb lattice with AB stacking geometry

We study some dynamic properties of the bilayer honeycomb lattice with AB stacking geometry in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. First, we obtain dynamic phases in the system and observe the paramagnetic (p), ferromagnetic (f), compensated (c) antiferromagnetic (af), surface ferromagnetic (sf) and mixed (m) phases. Besides, coexistence phase regions also exist in the system. Second, we investigate the thermal behavior of the dynamic order parameters. From these study, the natures (first- or second-order) of the transitions are characterized and the dynamic phase transition (DPT) points are presented. The DPTs are obtained and the dynamic phase diagrams (DPD) are constructed plane of the temperature versus the amplitude of the magnetic field. We investigate the effect of the frequency of the oscillating external magnetic field on the DPD.     

Two-dimensional and layered structures in the discrete φ4 model

The properties of phase transitions in two-dimensional and layered systems are investigated on the basis of a discrete φ⁴ model by numerical and analytical methods. The only parameter a of the discrete φ⁴ model determines the behavior of the system and makes it possible to investigate phase transitions ranging from transitions of the displacement type (a → +0) to order-disorder type (a → +∞). The behavior of a two-dimensional system is investigated in a wide range of values of the parameter a. The temperature dependences of the squared order parameter η²(T) and the phase transition temperature T _c as a function of the thickness N of the system are obtained for three characteristic values of the parameter a using the Monte Carlo method. The properties of phase transitions in the discrete φ⁴ model are investigated on the basis of the mean-field approximation and the independent-mode approximation. The results obtained in the numerical experiments are compared with the analytical approximations. It is shown that the mean-field approximation qualitatively describes the behavior of the phase-transition temperature T _c as a function of the thickness N of the system for a wide range of values of the parameter a, and the independent-mode approximation describes quantitatively, to within 5%, the results of the numerical simulation for small values of a.     

Holographic superconductor models in the non-minimal derivative coupling theory

We study a general class of holographic superconductor models via the Stu¨ckelberg mechanism in the non-minimal derivative coupling theory in which the charged scalar field is kinetically coupling to Einstein’s tensor. We explore the effects of the coupling parameter on the critical temperature, the order of phase transitions and the critical expo- nents near the second-order phase transition point. Moreover, we compute the electrical conductivity using the probe approximation and check the ratios ω g /T c for the different coupling parameters.     

Peculiarities of the critical dynamics in magnetically uniaxial PbFe<Subscript>12</Subscript>O<Subscript>19</Subscript> hexaferrite

The conditions under which the thermodynamic theory of the critical slowing-down of the order parameter relaxation rate describes the behavior of magnetically uniaxial crystals are formulated. Taking into account the formulated conditions, the peculiarities of the dynamic magnetic susceptibility and the critical slowing-down of the magnetization relaxation rate of PbFe₁₂O₁₉ in the vicinity of the Curie temperature are studied. The obtained experimental results agree well with the droplet model of phase transitions. Based on the experimental data, an estimated value of the correlation length for the magnetization in the temperature area of the critical slowing-down of the relaxation rate is obtained within the droplet model.     

一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.     

On the nature of the magnetic transition in a Mott insulator

Using a combination of exact enumeration and the dynamical mean-field theory (DMFT) we study the drastic change of the spectral properties, obtained in the half-filled two-dimensional Hubbard model at a transition from an antiferromagnetic to a paramagnetic Mott insulator, and compare it with the results obtained using the quantum Monte Carlo method. The coherent hole (electron) quasiparticle spin-polaron subbands are gradually smeared out when the AF order disappears, either for increasing Coulomb repulsion U at fixed temperature T, or for increasing T at fixed U. Within the DMFT we present numerical evidence (a continuous disappearence of the order parameter) suggesting that the above magnetic transition is second order both in two and in three dimensions.Received: 20 November 2004, Published online: 9 April 2004PACS: 71.30. + h Metal-insulator transitions and other electronic transitions - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 79.60.-i Photoemission and photoelectron spectraThis work is dedicated to Professor Ole Krogh Andersen on the occasion of his 60th birthday.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

The influence of chromium impurity centers on the critical properties of a weakly polar ferroelectric Li<Subscript>2</Subscript>Ge<Subscript>7</Subscript>O<Subscript>15</Subscript>

The Cr³⁺ EPR spectra of Li₂Ge₇O₁₅ (LGO) crystals are analyzed in the temperature range of the ferroelectric phase transition. The temperature dependence of the local order parameter is determined from the measured splittings of the EPR lines in the polar phase. The experimental critical exponent of the order parameter β=0.31 in the range from the phase transition temperature T _C to (T _C -T) ～ 40 K corresponds to the critical exponent of the three-dimensional Ising model. Analysis of the available data demonstrates that, away from the phase transition temperature T _C , the macroscopic and local properties of LGO crystals are characterized by a crossover from the fluctuation behavior to the classical behavior described in terms of the mean-field theory. The temperature dependence of the local order parameter for LGO: Cr crystals does not exhibit a crossover from the Ising behavior (β=0.31) to the classical behavior (β=0.5). This is explained by the defect nature of Cr³⁺ impurity centers, which weaken the spatial correlations in the LGO host crystal. The specific features of the critical properties of LGO: Cr³⁺ crystals are discussed within a microscopic model of structural phase transitions.     

Information Dynamics at a Phase Transition

We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of information in a lattice simulation of a Ginzburg–Landau model with a scalar order parameter coupled to a heat bath. The CE is built from the Fourier spectrum of fluctuations around the mean-field and reaches a minimum at criticality. In particular, we investigate the behavior of CE near and at criticality, exploring the relation between information and the emergence of ordered domains. We show that as the temperature is increased from below, the CE displays three essential scaling regimes at different spatial scales: scale free, turbulent, and critical. Together, they offer an information-entropic characterization of critical behavior where the storage and fidelity of information processing is maximized at criticality.