Bicritical Point Research Articles

Field theory of bicritical and tetracritical points. IV. Critical dynamics including reversible terms

This article concludes a series of papers [Folk, Holovatch, and Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)] where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here we give the complete two-loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The nonasymptotic analysis of the dynamic flow equations shows that due to cancellation effects the critical behavior is described, in distances from the critical point accessible to experiments, by the critical behavior qualitatively found in one-loop order. Although one may conclude from the effective dynamic exponents (taking almost their one-loop values) that weak scaling for the order parameter components is valid, the flow of the time-scale ratios is quite different, and they do not reach their asymptotic values.

Blume–Capel model on the antiferromagnetic fcc lattice

In the presence of a uniform external magnetic field, the spin-1 fcc antiferromagnetic Ising model in the four sub-lattice with the nearest-neighbor bilinear and crystal field interactions is investigated by using mean-field theory. The lattice is considered in blocks and each block contains 32 spins. While the central four spins forming a basic tetrahedron structure are allowed to fluctuate, the surrounding 28 spins take the mean-field values. The ground state phase diagram of the system is examined since it provides valuable information to make a prediction of the different phase diagram topologies. The phase diagrams are obtained on the reduced external field versus temperature, (H/|J|−kT/|J|), plane for selected crystal field interaction values from the ground state phase diagram and it is found that the system exhibits reentrant behavior and some special points such as tricritical, bicritical and triple points.

Multicriticality in smectic liquid crystals

A phenomenological model permitting a unified description of different types of smectic liquid crystalline phases including the hexatic-B phase has been developed. The model describes five different liquid crystalline phases: nematic (N), smectic-A (SmA), smectic-C (SmC), hexatic-B (HexB) and smectic-E (SmE). We observe various multicritical points among different smectic phases. General arguments are presented for the topologies of the phase diagrams in the vicinity of the SmA–SmC–HexB and N–SmA–SmC bicritical points and in the vicinity of the SmA–HexB–SmE, SmA–SmC–SmE and SmC–HexB–SmE triple points. The existence of the SmA–HexB, SmA–SmC and SmC–HexB tricritical points near the SmA–HexB–SmE, SmA–SmC–SmE and SmC–HexB–SmE triple points is discussed. Calculations based on this model agree qualitatively with the experiments.

Bicritical point in multi-bands inhomogeneous superconductors

Multi-band systems as inter-metallic and heavy fermion compounds have quasi-particles arising from different orbitals at their Fermi surface. Since these quasi-particles have different masses or densities, there is a natural mismatch of the Fermi wave-vectors associated with different orbitals. This makes these materials potential candidates to observe exotic superconducting phases as Sarma or FFLO phases, even in the absence of an external magnetic field. The distinct orbitals coexisting at the Fermi surface are generally hybridized and their degree of mixing can be controlled by external pressure. In this work we investigate the existence of an FFLO type of phase in a two-band BCS superconductor controlled by hybridization analyzing the phase diagram at finite temperature, the system has similarities to conventional FFLO phase induced by field but has an entirely different nature, like a presence of a bicritical point.

Evidence for a bicritical point in theXXZHeisenberg antiferromagnet on a simple cubic lattice

The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.

Solvable Phase Diagrams and Ensemble Inequivalence for Two-Dimensional and Geophysical Turbulent Flows

Using explicit analytical computations, generic occurrence of inequivalence between two or more statistical ensembles is obtained for a large class of equilibrium states of two-dimensional and geophysical turbulent flows. The occurrence of statistical ensemble inequivalence is shown to be related to previously observed phase transitions in the equilibrium flow topology. We find in these turbulent flow equilibria, two mechanisms for the appearance of ensemble equivalences, that were not observed in any physical systems before. These mechanisms are associated respectively with second-order azeotropy (simultaneous appearance of two second-order phase transitions), and with bicritical points (bifurcation from a first-order to two second-order phase transition lines). The important roles of domain geometry, of topography, and of a screening length scale (the Rossby radius of deformation) are discussed. It is found that decreasing the screening length scale (making interactions more local) surprisingly widens the range of parameters associated with ensemble inequivalence. These results are then generalized to a larger class of models, and applied to a complete description of an academic model for inertial oceanic circulation, the Fofonoff flow.

The effects of the next-nearest-neighbour density–density interaction in the atomic limit ofthe extended Hubbard model

We have studied the extended Hubbard model in the atomic limit.The Hamiltonian analysed consists of the effective on-site interactionU and the intersite density–density interactionsWij (both nearest-neighbour and next-nearest-neighbour). The model can be considered asa simple effective model of charge ordered insulators. The phase diagrams andthermodynamic properties of this system have been determined within the variationalapproach, which treats the on-site interaction term exactly and the intersite interactionswithin the mean-field approximation. Our investigation of the general case taking intoaccount for the first time the effects of longer-ranged density–density interaction (repulsiveand attractive) as well as possible phase separations shows that, depending on thevalues of the interaction parameters and the electron concentration, the systemcan exhibit not only several homogeneous charge ordered (CO) phases, but alsovarious phase separated states (CO–CO and CO–nonordered). One finds that themodel considered exhibits very interesting multicritical behaviours and features,including bicritical, tricritical, and critical end points and isolated critical points.

Wave packet dynamics of two extended Harper models

We study the wave packet dynamics of two extended Harper models by using the second moment M2(t) and probability distribution Wn(t) numerically. The dynamical behaviors of two extended Harper models in all phases, on all phase boundary lines, and at the bicritical points are studied. For the first extended Harper model, we find that the wave packet is of ballistic diffusion in two metal phases, localized in the insulator phase, and of anomalous diffusion on the phase boundary lines and at the bicritical point. We also find the dynamical behavior on the boundary line of the metal-metal phase transition is the same as that on the metal-insulator phase transition. The spreading at the bicritical point is different from that on the phase boundary lines. For the second extended Harper model, we find that the wave packet is of ballistic diffusion in the metal phase, localized in the insulator phase, and of anomalous diffusion in the critical phase, on the phase boundary lines, and at the bicritical point. We also find the dynamical behavior on the boundary line of the critical-metal phase transition is similar to that at the bicritical point and the critical-insulator phase transition, but different from that of the metal-insulator phase transition.

Pressure-induced bicritical point in UPd2Si2

We have studied the effects of pressure on the incommensurate (IC)-commensurate (C) antiferromagnetic (AFM) phase transition of UPd2Si2 by measuring the electrical resistivity up to 4.21 GPa. We observed that the low-temperature C-AFM (type-I) phase expands and prevails over the IC-AFM phase as pressure is increased. The obtained pressure-temperature phase diagram strongly suggests the existence of a novel bicritical point, more specifically, the so-called Lifshitz point at Pc ~ 3.4 GPa, where magnetic modulation continuously changes from IC to C.

Magnetic phases of the quasi-two-dimensional compoundsFexCo1 − xTa2O6

We report new results on the magnetic properties of theFexCo1 − xTa2O6 series of compounds. Essentially using neutron-diffraction andmagnetic measurements we study, in more detail, the low-x limit of thetemperature versus x phase diagram, where a new bicritical point is observed. The complete phase diagramshows three different magnetic phases at low temperature, for a high, intermediate and verylow iron content. These phases consist of distinct antiferromagnetic orderings, characterizedby different pairs of propagation vectors. We obtain information about the intraplaneexchange interactions by fitting a high-temperature series of the magnetic susceptibility.Here we improve on a previously employed model, showing that two non-equivalentnext-nearest-neighbor interactions must be taken into account in order to allow forin-plane magnetic orderings that are consistent with the neutron-diffraction results.

Phase diagram for a two-dimensional, two-temperature, diffusiveXYmodel

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature conserved order parameter XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin texture order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent φ=2.52±0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.

The (k B T C/zJ,k) Phase Diagram for the D/J=1 on the Four-Dimensional Blume–Emery–Griffiths (BEG) Model

The 4-d spin-1 Ising (BEG) model has been simulated using a cellular automaton (CA) cooling algorithm improved from the 3-d BEG model algorithm for the four-dimensional hypercubic lattices. The ground state diagram (k,d) of the 4-d BEG model has ferromagnetic (F), quadruple (Q) and staggered quadruple (SQ) ordering regions. The simulations have been made in the −3≤k=K/J≤1 interval through the d=1 line for L=18 lattice size. The (k B T C/zJ,k) phase diagram has been obtained through the d=1 phase line. The results show that the model has a bicritical point (BCP) as in d<4 dimensions. The phase diagram has been separated to the three regions of the staggered quadruple (SQ), the ferromagnetic (F) and the paramagnetic (P) cases.

Nematic-smectic-A-smectic-C multicritical point: An alternative model

A new Landau-type phenomenological free-energy function to describe the nematic-smectic-A transition, smectic-A-smectic-C transition and nematic-smectic-C transition is proposed. The influence of pressure on the these phase transitions is discussed by varying the coupling between various order parameters. The phase diagram of the thermodynamic parameters is studied and a possible nematic-smectic-A-smectic-C bicritical point is predicted. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a bicritical point is observed in the phase diagram. The obtained topology of the pressure-temperature phase diagram is consistent with experimental results.

The spin- [formula omitted] sandwiched trilayer Bethe lattices

The Ising model for the spin- ( 1 , 1 2 , 1 ) sandwiched trilayer Bethe lattices is investigated in terms of the recursion relations with either ferromagnetic (FM) or antiferromagnetic (AFM) type of bilinear interactions between the nearest-neighbor (NN) spins. In addition to the ground-state (GS) phase diagrams, the thermal variations of the order-parameters, spin–spin correlation functions and free energies are studied; therefore, different topological temperature-dependent phase diagrams are obtained. It was found that the system exhibits second- and first-order phase transitions. The bicritical, critical end and multicritical points, and the stable and unstable tricritical points are observed in addition to the reentrant behavior for the coordination numbers q = 3 , 4 and 6.

Antiferromagnetic critical pressure inURu2Si2under hydrostatic conditions

The onset of antiferromagnetic order in URu2Si2 has been studied via neutron diffraction in a helium pressure medium, which most closely approximates hydrostatic conditions. The antiferromagnetic critical pressure is 0.80 GPa, considerably higher than values previously reported. Complementary electrical resistivity measurements imply that the hidden order-antiferromagnetic bicritical point far exceeds 1.02 GPa. Moreover, the redefined pressure-temperature phase diagram suggests that the superconducting and antiferromagnetic phase boundaries actually meet at a common critical pressure at zero temperature.

Sandwiched trilayer of Bethe lattices in the form of spin-(1/2,1,1/2)

The sandwiched trilayer of Bethe lattices in the form of the spins with spin-(1/2,1,1/2) Ising model is studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic type bilinear interactions between the nearest-neighbor (NN) spins. The ground-state (GS) phase diagrams are obtained and it was found that the model presents six different GS phase configurations. In order to obtain the phase diagrams, the thermal variations of the order-parameter, spin–spin correlation functions and free energy are analyzed and different topological phase diagrams are obtained. It was found that the system exhibits different critical behaviors such as, second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3,4 and 6.

Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism inURu2Si2Observed by Larmor Diffraction

We report for the first time simultaneous microscopic measurements of the lattice constants, the distribution of the lattice constants, and the antiferromagnetic moment in high-purity URu(2)Si(2), combining Larmor and conventional neutron diffraction at low temperatures and pressures up to 18 kbar. Our data demonstrate quantitatively that the small moment in the hidden order (HO) of URu(2)Si(2) is purely parasitic. The excellent experimental conditions we achieve allow us to resolve that the transition line between HO and large-moment antiferromagnetism (LMAF), which stabilizes under pressure, is intrinsically first order and ends in a bicritical point. Therefore, the HO and LMAF must have different symmetry, which supports exotic scenarios of the HO such as orbital currents, helicity order, or multipolar order.

Unbiased Monte Carlo simulations of realistic models: Colossal magnetoresistive manganites

We investigate the one-orbital model for manganites with cooperative phonons and superexchange coupling JAF via large-scale Monte Carlo (MC) simulations. Results for two-orbitals are also briefly discussed. Focusing on an the realistic electronic density n=0.75, a regime of competition between ferromagnetic (FM) metallic and charge-ordered (CO) insulating states was identified in the finite temperature phase diagram. In the vicinity of the associated bicritical point, colossal magnetoresistance (CMR) effects were observed. The CMR magnitude is much larger than recently reported when randomly distributed polarons form the competing insulator. The appearance of CMR is associated with the development of short-distance correlations among polarons, above the spin ordering temperatures, resembling the charge arrangement of the low-temperature CO state. We present calculations of charge-charge correlations as well as typical Monte Carlo snapshots to support this view.

Phase diagram and critical behavior of the square-lattice Ising model with competing nearest-neighbor and next-nearest-neighbor interactions

Using the parallel tempering algorithm and graphics processing unit accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, re-entrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.

Square lattice hard-core bosons within the random phase approximation

Using random phase approximation we build finite-temperature phase diagrams and calculate thermodynamic functions of a square lattice hard-core boson model with nearest (nn) and next-nearest-neighbor (nnn) interactions in terms of equivalent to it an anisotropic spin-1/2 $XXZ$ model in a magnetic field. The system undergoes liquid-solid phase transitions that can be either of the first or second order. Depending on the hopping value and ratio between nn and nnn interactions the system displays two types of critical behavior. The line of the first-order transitions terminates in a bicritical end point inside the solid phase or ends in a tricritical point continuously giving way to the second-order phase transition line. The connection of the hopping and the ratio between the nn and nnn interactions with criticality of the system is investigated. The critical line separating the regions of specific critical behavior is built. Reentrant liquid-solid-liquid phase transitions are found and discussed.