Quantum phase transitions in Bose–Fermi systems

Quantum phase transitions in a system of N bosons with angular momentum L = 0, 2 (s, d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially the critical value of the control parameter at which the phase transition occurs. Experimental evidence for the U(5)–SU(3) (spherical to axially-deformed) transition in odd–even nuclei is presented.     

Quantum Phase Transition Like Phenomenon in a Two-Qubit Yang-Baxter System

The quantum phase transition for the “q-deformed” Yang-baxter Hamiltonian has been discussed. The calculation shows when the deformed parameter q approaches 1, there exists a quantum critical point for spectral parameter θ. In this Yang-Baxter system, quantum entanglement and the geometric phase can characterize quantum phase transition.     

Mean Field Analysis of Low–Dimensional Systems

For low–dimensional systems, (i.e. 2D and, to a certain extent, 1D) it is proved that mean–field theory can provide an asymptotic guideline to the phase structure of actual systems. In particular, for attractive pair interactions that are sufficiently “spead out” according to an exponential (Yukawa) potential it is shown that the energy, free energy and, in particular, the block magnetization (as defined on scales that are large compared with the lattice spacing but small compared to the range of the interaction) will only take on values near to those predicted by the associated mean–field theory. While this applies for systems in all dimensions, the significant applications are for d = 2 where it is shown: (a) If the mean–field theory has a discontinuous phase transition featuring the breaking of a discrete symmetry then this sort of transition will occur in the actual system. Prominent examples include the two–dimensional q = 3 state Potts model. (b) If the mean–field theory has a discontinuous transition accompanied by the breaking of a continuous symmetry, the thermodynamic discontinuity is preserved even if the symmetry breaking is forbidden in the actual system. E.g. the two–dimensional O(3) nematic liquid crystal. Further it is demonstrated that mean–field behavior in the vicinity of the magnetic transition for layered Ising and XY systems also occurs in actual layered systems (with spread–out interactions) even if genuine magnetic ordering is precluded.     

Spatial structures and dynamics of kinetically constrained models of glasses

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices, a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density v, the spacing Xi between mobile elements diverges exponentially or faster in 1/v. Within the mobile elements, the dynamics is intrinsically cooperative, and the characteristic time scale diverges faster than any power of 1/v (although slower than Xi). The tagged-particle diffusion coefficient vanishes roughly as Xi(-d).     

Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System

We study a system of rods onℤ², with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N = 2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.     

Comments on the analytical solutions of the sticky hard rod model

The result that follows by taking the Percus-Yevick (PY) approximation from the exact analysis of the sticky hard rod model is shown to differ from that previously obtained by Tago, Y., and Katsura, S., 1975, Can. J. Phys. 53, 2587, and the correct PY compressibility and virial equations of state are given. It is also shown that Born-Green theory yields the exact solution for the sticky hard rod fluid.     

Molecular models for ferroelectric liquid crystals with conventional and anomalously weak layer contraction

A molecular theory of the ferroelectric smectic C* phase has been developed using the simple model of a chiral molecule composed of a uniaxial core and a pair of off-center nonparallel dipoles which determine molecular chirality and polarity. The interaction between uniaxial cores is modeled by a rather general effective potential which can be used to describe smectic materials with both conventional and anomalously weak layer contraction in the smectic C* phase. Spontaneous polarization, tilt, and layer spacing are calculated numerically as functions of temperature, and it is shown that the variation of the polarization generally deviates from that of the tilt angle. It is shown that this deviation is more pronounced in smectic materials tilting with low layer contraction which corresponds to existing experimental data. The model has been used to reproduce qualitatively the experimental data for polarization, tilt and layer spacing for two similar mixtures exhibiting conventional and anomalously weak layer contraction. The polarization and the tilt are also calculated in the case when the smectic A-smectic C* transition is characterized by the biaxial primary order parameter.     

The measurement of solid–liquid interfacial energy in colloidal suspensions using grain boundary grooves

Interfacial energy is a fundamental physiochemical property of any multi-phase system. Among the most direct approaches for determining solid–liquid interfacial energy is a technique based on measuring the shape of grain boundary grooves in specimens subjected to a linear temperature gradient. This technique was adapted to crystallizing colloids in a gravitational field. Such colloids exhibit a freezing–melting phase transition and are important not only as self-assembling precursors to photonic crystals, but also as physical models of atomic and molecular systems. The grain boundary groove technique was tested using suspensions of sterically stabilized poly(methyl methacrylate) spheres, which have been shown to closely approximate the hard sphere potential. Whereas isotropic models did not fit grain boundary groove data well, the capillary vector model, which is suitable for both isotropic and anisotropic surface energies, produced γ₁₁₀?=?0.58?±?0.05 k _B T/σ². This value of interfacial energy is in agreement with many of the published values for hard spheres, supporting the validity of our grain boundary groove technique adaptations to colloidal systems in a gravitational field. Finally, kinks observed in groove profiles suggest a minimum anisotropy parameter of ε?=?0.029 for hard spheres.     

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell’s theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell’s theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.     

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the τ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for τ, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the τ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts τ ∼ d ³. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the τ parameter should be of order unity as d tends to infinity.     

Rigid rod adsorption including long-range dispersion interactions

The Caillé-Ågren analysis of rigid rod adsorption is extended by applying the van Kampen theory of condensation to include long-range dispersion interactions between the adsorbed rods. We discuss in greater detail the characteristics of the phase transition predicted by Caillé and Ågren between states having an isotropic and anisotropic distribution of rods adsorbed parallel to the surface. The maximum density range over which the anisotropic adsorbed phase is stable is determined as a function of the length-to-breadth ratio x of the rigid rods and the strength of the anisotropic dispersion energy. Critical surface adhesion and anisotropic dispersion energies necessary for anisotropic adsorption are also obtained as a function of x. In agreement with Caillé and Ågren the isotropic-anisotropic transition for rigid rod adsorption with attractive forces present is found to be second order. We also discuss the spreading pressure-density or area per molecule isotherms obtained for adsorbed rods having various values of x and surface adhesion and dispersion energies. Whenever feasible we compare our results with the spreading pressure isotherms obtained for monolayers of lyotropic molecules on either aqueous or mercury subphases and obtain qualitative agreement. In particular, the critical density and pressure associated with the two dimensional adsorbed gas-liquid condensation for rigid rods with x = 10 gives reasonable agreement with the critical constants observed by Hawkins and Benedek and Kim and Cannell for the corresponding condensation of pentadecanoic acid monolayers on neutral and acidified aqueous subphases. This agreement suggests that considerable dimerization of the pentadecanoic acid molecules may occur on aqueous surfaces.     

Non-Douglas–Kazakov phase transition of two-dimensional generalized Yang–Mills theories

In two-dimensional Yang–Mills and generalized Yang–Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density, the value of which should everywhere be between zero and one. This density itself is determined by means of a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas–Kazakov phase transition. In generalized Yang–Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas–Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with the order of the phase transition not equal to three. A class of these non-typical models is also studied.     

Critical behavior of RMn2O5 oxides near the magnetic phase transition to a structure incommensurate in two spatial directions

A phase transition from the paramagnetic state to the long-period magnetic structure in RMn₂O₅ oxides with the star of the wave vector determining the incommensurability of long-range magnetic order in two spatial directions has been investigated. An effective Hamiltonian of the system that allows one to describe this transition in the framework of the renormalization group approach has been constructed. It has been shown that there is a stable critical point of transformations of this group at which there occurs a second-order phase transition. The critical indices have been found. The obtained results have been compared with the results for phase transitions occurring in these oxides in accordance with the star of the wave vector, which provides incommensurability in one of the spatial directions. It has been found that fluctuations of the four-component order parameter due to the low spatial symmetry of these compounds do not change the order of the phase transition, which was found in terms of the Landau theory.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

三维钻石型等级晶格上量子Heisenberg系统的临界性质

利用重整化群方法,研究了三维钻石型等级晶格上的各向异性量子Heisenberg模型,获得了系统的相图和临界性质. 结果表明:对于铁磁系统,在各向同性Heisenberg极限下,系统存在有限温度的相变,并计算了系统的序参量和临界指数; 对于反铁磁系统,在各向同性Heisenberg极限下,临界温度不等于零,在临界线上不存在重入行为.     

Magnetic phase transitions,soliton lattices,and electric polarization in <Emphasis Type="Italic">R</Emphasis>Mn<Subscript>2</Subscript>O<Subscript>5</Subscript> multiferroics

The magnetic phase transitions in RMn₂O₅ oxides were analyzed. It was shown that the transition from the paramagnetic phase to the incommensurate phase is described by not only the basic magnetic parameter but also an associated order parameter: electric polarization along the y axis of the crystal. It was established that the antiferromagnetic-incommensurate phase transformation is a second-order phase transition, accompanied by a decrease in electric polarization.     

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.     

Induced anticlinic ordering and nanophase segregation of bow-shaped molecules in a smectic solvent

Recent experiments indicate that doping low concentrations of bent-core molecules into calamitic smectic solvents can induce anticlinic and biaxial smectic phases. We have carried out Monte Carlo simulations of mixtures of rodlike molecules (hard spherocylinders with length/breadth ratio L(rod)/D = 5) and bow-shaped molecules (hard spherocylinder dimers with length/breadth ratio L(ban)/D = 5 or 2.5 and opening angle psi). We find that a low concentration ( 3%) of L(ban)/D = 5 dimers induces anticlinic ( SmC(A)) ordering in an untilted smectic ( SmA) phase for 100 < or = psi < 150. For L(ban)/D = 2.5, no tilted phases are induced. However, with decreasing psi we observe a sharp transition from intralamellar nanophase segregation (bow-shaped molecules segregated within smectic layers) to interlamellar nanophase segregation (bow-shaped molecules concentrated between smectic layers) near psi = 130.