Ordering and phase transitions in ising systems with competing short range and dipolar interactions

As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ ²/a ³. ForJa ³/µ ²Ja ³/µ ²<0.1270 the ground state consists of ferromagnetic rows (in spin direction) arranged antiferromagnetically in the plane perpendicular to it. AtJa ³/µ ²=0.1279 the structure changes to a layered antiferromagnetic structure with a twocomponent order parameter, while forJa ³/µ ²>0.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa ³/µ ² where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero. The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa ³/µ ² of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.     

Phase transitions in random uniaxial systems with dipolar interactions

The critical behaviour of random uniaxial ferromagnetic (ferroelectric) systems with both short range and long range dipolar interactions is investigated, using the field theoretic renormalization method of Brézin et al. for the free energy above and below the transition pointT _c. The randomness is due to externally introduced fluctuations in the short range interactions (quenched case) or (and) magneto-elastic coupling to the lattice (annealed case). Strong deviations in the critical behaviour with respect to the pure systems are found. In the quenched case e.g. the specific heatC and the coefficientf ₂ (ofM ³ in the equation of state, whereM is the magnetization) change fromC |ln|t^1/3,f ₂ |ln|t^–1 in the pure system toC is the reduced temperature andA _±,C _± are constants) in the random situation. This change should e.g. be experimentally observable by deuterization of the ferroelectric tri-glycine sulfate where the logarithmic behaviour off ₂ has already been detected in the pure case. For nonvanishing magnetoelastic coupling a complex critical behaviour is obtained and discussed. We find the interesting result that if both quenched randomness and a weak magnetoelastic coupling are present the quenched random critical behaviour dominates in the close vicinity ofT _c. Finally the influence of the magnetoelastic coupling on the longitudinal phonons in investigated and it is found that the relative changes in the corresponding elastic constant and structure factor are proportional to the specific heat and the wavevector dependent energy-energy correlation function respectively, suggesting new experiments.     

The effects of forcing and dissipation on phase transitions in thin granular layers

Recent experimental and computational studies of vibrated thin layers of identical spheres have shown transitions to ordered phases similar to those seen in equilibrium systems. Motivated by these results, we carry out simulations of hard inelastic spheres forced by homogenous white noise. We find a transition to an ordered state of the same symmetry as that seen in the experiments, but the clear phase separation observed in the vibrated system is absent. Simulations of purely elastic spheres also show no evidence for phase separation. We show that the energy injection in the vibrated system is dramatically different in the different phases, and suggest that this creates an effective surface tension not present in the equilibrium or randomly forced systems. We do find, however, that inelasticity suppresses the onset of the ordered phase with random forcing, as is observed in the vibrating system, and that the amount of the suppression is proportional to the degree of inelasticity. The suppression depends on the details of the energy injection mechanism, but is completely eliminated when inelastic collisions are replaced by uniform system-wide energy dissipation.     

Birefringence and phase transitions in liquid crystals

The birefringence of liquid-crystalline phases is the result of the parallel order of molecules exhibiting a polarizability anisotropy. The magnitude and sign of the birefringence are determined by the structure and order of the liquid-crystalline phase types as well as by the polarizability properties of the constituent molecules. The characteristic change of the birefringence at phase transitions between liquid-crystalline phases indicates more or less pronounced structural changes. The temperature dependence of the birefringence is due to the temperature change of the molecular order.

It is shown that the structural variety of the liquid crystalline state is reflected by a big variety of their optical anisotropy properties.     

Ordering and phase transitions in liquid crystals

Structures and properties of different types of liquid crystals are discussed from a uniform point of view. Apart from the traditional mesophases (nematics, cholesterics, smectics), some new examples, including polymeric, metalloorganic and ferromagnetic liquid crystals, are also investigated. Systems with several macroscopic scales on which the type of ordering may differ, are described and analysed. Phase transitions and certain types of critical behaviour in different liquid crystals are studied.     

Phase transitions in hybrid SFS structures with thin superconducting layers

Features of a phase transition between 0 and π states in superconductor/ferromagnet/superconductor (SFS) Josephson structures with thin superconducting layers and a ferromagnetic barrier are studied experimentally and theoretically. The dependence of the critical temperature T_c of a transition of the hybrid structure to a superconducting state on the thickness of superconducting layers d_s is analyzed by a local method involving measurements of the nonlinear microwave response of the system by a near-field probe. An anomalous increase in the measured temperature T_c at the reduction of the thickness d_s is detected and is attributed to the 0-π transition.     

Phase transitions in hybrid SFS structures with thin superconducting layers

Calculations of critical temperature T _c of the phase transition to superconducting state of a superconductor/ ferromagnet/superconductor (SFS) hybrid structure with proximity effect is performed on the base of linearized Usadel equations. It is shown that the proximity effect between S and F metals and the exchange interaction can induce an inhomogeneous superconducting state with longitudinal to layers Δ _∝ exp(ipz) modulation of the superconductivity order parameter, which is characterized by nonzero value of the wave number p, describing the Larkin–Ovchinnikov–Fulde–Ferrell instability. Influence of this instability on transitions between 0- and π-states of the SFS structure is studied. It is shown that the 0–π transition is accompanied by a nonmonotonic dependence of both the critical temperature T _c and the effective penetration depth Λ of the magnetic field into the hybrid structure on the characteristic size of the ferromagnetic region.     

Multipolar phase transitions in magnetic crystals

We have studied the possibility of successive multipolar phase transitions in magnetic crystals. A Hamiltonian including various (l ? 4) multipolar interactions is treated in the molecularfield approximation. If each interaction is introduced with its characteristic symmetry, three successive phase transitions at most are found in the absence of any crystalline field anisotropy.     

Reentrant phase transitions in liquid crystals

A comprehensive review of the recent developments regarding the phenomenon of reentrant phase transitions (RPT) in liquid crystals is presented. In addition to liquid crystals this phenomenon has been observed in amazingly diverse systems. A critical assessment of the experimental investigations concerning single and multiple reentrances is given. A brief account of the theoretical efforts is also given. The article ends with the identification of the factors which impede the proper understanding of the phenomenon.     

Structural phase transitions in crystals with coupled softening modes

Structural phase transitions in crystals with more than one softening phonon mode are investigated in mean field theory. It is found that, for negative coupling energies between two modes, the critical temperature of each mode increases. For large coupling, both modes become soft at the same temperature and the phase transition becomes of first order. For positive coupling energies, the critical temperatures rapidly go to zero but not for the same value of coupling. A phase diagram is given and a possible application to alkali-TCNQ salts is discussed.     

Crystal-glass phase transitions in the adatom layers

Phase transitions in the two-dimensional crystalline films adsorbed onto an imperfect substrate (with impurities and defects) are analyzed. It is shown that the phase transition from the commensurate long-range-order (LRO) crystal to the glass state occurs with increase of impurity concentration. The orientational correlation function is shown to tend algebraically to zero at large distances in the glass state. The influence of defects on the phase transition from the LRO-commensurate crystal to the disordered state at the definite temperature T_m is considered.     

Field-induced phase transitions in antiferroelectric liquid crystals

A theoretical study is made of the process by which an antiferroelectric smectic liquid crystal undergoes a field-induced transition to ferroelectric alignment. We find that for cells of moderate thickness the initial departure from antiferroelectric alignment occurs as a continuous Fréedericksz transition. The following transition from partial alignment to complete ferroelectric ordering may occur as either a first-order or continuous transition, depending on the relative strength of some of the model parameters. The case where the transition is continuous provides a possible mechanism for some recently observed thresholdless transitions in these systems.     

Polarization interaction and phase transitions in crystals with two interacting subsystems

The influence of the polarization interactions on the state and phase transitions in magnetic-ordered and dielectric crystals with two interacting order parameters has been investigated. Consideration is given to the case when the interaction in one of the subsystems is considerably weaker than that in the other subsystem. It is demonstrated that the polarization interactions in the weak subsystem can substantially affect the state and the character of phase transitions in the strong subsystem. These interactions can bring about the disordering (formation of the random-field state or the state of spin glass) in the critical region near the second-order phase transition in the main subsystem and also the smearing of the phase transition. At the same time, the polarization interactions can give rise to the ordered and disordered states in the weak subsystem.     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

First-order magnetic phase transitions in thin films

Using the simple Landau model, we discuss near-surface magnetic effects for thin films corresponding to first-order phase transitions. The size effects observed in ultrathin ferroelectric films are in agreement with this theoretical interpretation. The presence of a weak external field is also formulated. The text was submitted by the authors in English.     

面心立方(001)方向AB合金薄膜表面层的有序无序相变

采用平均场近似方法对两组元面心立方合金薄膜的有序无序相转变过程进行模拟计算,结果表明,合金薄膜的有序无序相变受薄膜层数奇偶性的影响.薄膜层数奇偶性不同,会导致薄膜具有不同的相结构和热力学性质.在弱表面偏析作用下,对于偶数层薄膜,由于薄膜边界对称性破缺,对应体组分x=0.5的化学势区间,偶数层薄膜有序无序相变过程中出现了中间温度相和浸润现象.而奇数层薄膜的有序无序相变类似体材料的相变.在强表面偏析作用下,由于受表面偏析作用和有限尺寸效应影响,对应体组分x=0.5的化学势区间,奇数层薄膜中出现AB(AB)nA相,它不存在严格热力学意义上的有序无序相变.     

Dynamics and phase transitions in biased ladder systems with magnetic flux

The ground states and the dynamics of a biased two-leg flux ladder in the presence of a gravitational field are discussed. In the absence of the gravitational field, the ground states and the critical condition of phase transition are obtained analytically. We identify the Meissner phase, Vortex phase, and interestingly, two new Plane Wave phases, that break both $Z_2$ and time-reversal symmetry, characterized by the imbalance particle density distribution, asymmetry double well energy band structure in Plane Wave I (PWI) phase and asymmetry single well energy band structure in Plane Wave II (PWII) phase, respectively. In the presence of a longitudinal dc gravitational field, rich chiral Bloch oscillation and Landau-Zener tunneling are predicted theoretically and confirmed numerically. The characteristics of the chiral Bloch oscillation can distinguish the novel phases intuitively. Our work gives an interesting way to discuss the quantum phase transitions in a dynamical way.     

Acoustic studies of phase transitions in crystals and nanocomposites

A brief review of acoustic studies of phase transitions in crystals (ferroelectric, ferroelastic, and superionic ones) and nanostructured composite materials made on the basis of porous matrices is presented. The studies were carried out at the Laboratory of Quantum Acoustics and Ultrasonic Spectroscopy of the St. Petersburg State University.