Global Phase Diagram Research Articles

The analysis of traveling wave structures and chaos of the cubic–quartic perturbed Biswas–Milovic equation with Kudryashov's nonlinear form and two generalized nonlocal laws

The cubic–quartic perturbed Biswas–Milovic equation, which contains Kudryashov's nonlinear form and two generalized nonlocal laws, has been explored qualitatively and quantitatively, as demonstrated in the present work. The research methods used include the complete discrimination system for polynomial method and the trial equation method. The results show that the Hamiltonian has the conservation property, and the global phase diagrams obtained via the bifurcation method reveal the existence of periodic and soliton solutions. Furthermore, we fully classify all the single traveling wave solutions to substantiate our findings, covering singular solutions, solitons, and Jacobian elliptic function solutions. We analyze their topological stabilities and present two‐dimensional graphs of solutions. We also delve deeper into the dynamic system by incorporating the perturbation item to explore the chaotic phenomena associated with the equation. These outcomes are valuable for studying the propagation of high‐order dispersive optical solitons and have potential applications in optimizing optical communication systems to improve efficiency.

Metal-insulator transition of spinless fermions coupled to dispersive optical bosons

Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model.

Global Dynamics of a Holling-II Amensalism System with a Strong Allee Effect on the Harmful Species

In this study, we discuss the global dynamics of the Holling-II amensalism model for a strong Allee effect of harmful species. We discuss the existence and stabilization of the extinction equilibria, exclusion equilibria, coexistence equilibria, and infinite singularities by analyzing the presence and stabilization of the system characteristics in terms of the possibilities and correspondences in the model when the death rate of the injured species is used as a threshold value. Also, we find that the two equilibrium points in the first quadrant are effective in proving that the model does not have globally stabilizing features and obtain two critical conditions and their corresponding global phase diagrams. Finally, we explore the weak Allee effect of the victim species, and using the analysis from numerical simulations, we recapitulate the analysis and dynamics of the model in equilibrium.

Capillary condensation between nonparallel walls.

We study the condensation of fluids confined by a pair of nonparallel plates of finite height H. We show that such a system experiences two types of condensation, termed single and double pinning, which can be characterized by one (single-pinning) or two (double-pinning) edge contact angles describing the shape of menisci pinned at the system edges. For both types of capillary condensation, we formulate the Kelvin-like equationand determine the conditions under which the given type of condensation occurs. We construct the global phase diagram revealing a reentrant phenomenon pertinent to the change of the capillary condensation type upon varying the inclination of the walls. Asymptotic properties of the system are discussed and a link with related phase phenomena in different systems is made. Finally, we show that the change from a single- to a double-pinned state is a continuous transition, the character of which depends on the wetting properties of the walls.

Impact of Limestone Surface Impurities on Quicklime Product Quality

Quicklime is produced through the thermal processing of limestone in industrial kilns. During quarry operations, fine particulate quarry dust adheres to limestone lump surfaces, increasing the bulk concentration of impurities in limestone products. During thermal processing in a kiln, impurities such as Si, Mg, Al, Fe, and Mn react with Ca, reducing quicklime product quality. Which reactant phases are formed, and the extent to which these result in a reduction in quality, has not been extensively investigated. The present study investigated as-received and manually washed limestone product samples from two operational quarries using elemental compositions and a developed predictive multi-component chemical equilibrium model to obtain global phase diagrams for 1000–1500 °C, corresponding to the high-temperature zone of a lime kiln, identifying phases expected to be formed in quicklime during thermal processing. The results suggest that impurities found on the surface of the lime kiln limestone feed reduce the main quality parameter of the quicklime products, i.e., calcium oxide, CaO (s), content by 0.8–1.5 wt.% for the investigated materials. The results also show that, in addition to the effect of impurities, the quantity of CaO (s) varies greatly with temperature. More impurities result in more variation and a greater need for accurate temperature control of the kiln, where keeping the temperature below approximately 1300 °C, that of Hatrurite formation, is necessary for a product with higher CaO (s).

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

Approximate Damped Oscillatory Traveling Wave in Viscous Compressible Fluid With Capillary Effect

We convert the viscous compressible fluid equations with capillary effect into the equivalent planar dynamical system and illustrate the global qualitative phase diagrams corresponding to its bounded orbits by the qualitative theory of ordinary differential equations. From the evolutionary relationship of bounded orbits in global qualitative phase diagrams and the correspondence between the bounded orbit and traveling wave, we discover the evolutionary rule of the profile of the traveling wave as the viscous coefficient varying and the forming reason for the damped oscillatory traveling wave. Further, we construct the analytical approximate explicit expression of the damped oscillatory traveling waves in accordance with the forming reason and prove its error decreases in exponential form. Finally, we compare the approximate damped oscillatory traveling wave with the numerical solution. The result shows they fit well.

Study on dynamic features and traveling wave solutions of perturbed nonlinear Biswas–Milovic equation combining Kudryashov's law of refractive index

This article mainly explores the Biswas–Milovic equation containing Kudryashov's refractive index law and nonlinear perturbation terms. We take the complete discrimination system for polynomial method and the trial equation method to implement qualitative and quantitative studies for the equation. We verify that the Hamiltonian of the dynamic system is conserved and apply the complete discrimination system of polynomial method to give the associated global phase diagrams, which are qualitatively analyzed to illustrate the presence of periodic solutions and solitons. In addition, we gain a classification of all single traveling wave solutions, provide optical wave patterns with specific parameters and validate the above findings.

Rotational symmetry breaking in superconducting nickelate Nd0.8Sr0.2NiO2 films

The infinite-layer nickelates, isostructural to the high-Tc cuprate superconductors, have emerged as a promising platform to host unconventional superconductivity and stimulated growing interest in the condensed matter community. Despite considerable attention, the superconducting pairing symmetry of the nickelate superconductors, the fundamental characteristic of a superconducting state, is still under debate. Moreover, the strong electronic correlation in the nickelates may give rise to a rich phase diagram, where the underlying interplay between the superconductivity and other emerging quantum states with broken symmetry is awaiting exploration. Here, we study the angular dependence of the transport properties of the infinite-layer nickelate Nd0.8Sr0.2NiO2 superconducting films with Corbino-disk configuration. The azimuthal angular dependence of the magnetoresistance (R(φ)) manifests the rotational symmetry breaking from isotropy to four-fold (C4) anisotropy with increasing magnetic field, revealing a symmetry-breaking phase transition. Approaching the low-temperature and large-magnetic-field regime, an additional two-fold (C2) symmetric component in the R(φ) curves and an anomalous upturn of the temperature-dependent critical field are observed simultaneously, suggesting the emergence of an exotic electronic phase. Our work uncovers the evolution of the quantum states with different rotational symmetries in nickelate superconductors and provides deep insight into their global phase diagram.

Global Ashkin–Teller phase diagrams in two and three dimensions: Multicritical bifurcation versus double tricriticality—endpoint

The global phase diagrams of the Ashkin–Teller model are calculated in d=2 and 3 by renormalization-group theory that is exact on the hierarchical lattice and approximate on the recently improved Migdal–Kadanoff procedure. Three different ordered phases occur in the dimensionally distinct phase diagrams that reflect three-fold order-parameter permutation symmetry, a closed symmetry line, and a quasi-disorder line. First- and second-order phase boundaries are obtained. In d=2, second-order phase transitions meeting at a bifurcation point are seen. In d=3, first- and second-order phase transitions are separated by tricritical and critical endpoints.

Thermal hysteresis of mesoscopic phase transitions in fluid metals: From tantalum to aluminum and gold with their critical points and non-mean-field global diagrams

The light soft metal – Al-IIIB in Periodic Table and the heavy soft metal – Au-IB were analyzed within the predictive model of fluctuation–thermodynamics (FT). The similar extrapolative approach was applied for re-establishing of the global phase diagram and non-mean-field criticality of the refractory heavy and rigid tantalum Ta-VA earlier. The revealed then correspondence between the onset point of nano-droplets at atmospheric pressure and the point of instability, observable at much higher pressures by the fast dynamic measurements, found its confirmation for the considered metals as well. It may indicate the universality of the mentioned “dew”-point for any elements and compounds. The mesoscopic nanoscaled time- and length- simultaneous consideration matters especially for all metallic vapors at sub-atmospheric pressures and temperatures beneath the normal boiling one. The FT-predicted critical points of Al and Au are consistent with the available low-temperature thermostatic and rapid dynamic experimental data.

Surface Phase Diagrams for Wetting with Long-Ranged Forces.

Recent density functional theory and simulation studies of wetting and drying transitions in systems with long-ranged, dispersionlike forces, away from the near vicinity of the bulk critical temperature T_{c}, have questioned the generality of the global surface phase diagrams for wetting, due to Nakanishi and Fisher, pertinent to systems with short-ranged forces. We extend these studies deriving fully analytic results which determine the surface phase diagrams over the whole temperature range up to T_{c}. The phase boundaries, order of, and asymmetry between the lines of wetting and drying transitions are determined exactly showing that they always converge to an ordinary surface critical point. We highlight the importance of lines of maximally multicritical wetting and drying transitions, for which we determine the exact critical singularities.

Merged Potts-clock model: Algebraic and conventional multistructured multicritical orderings in two and three dimensions.

A spin system is studied with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalization-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: Conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first- and second-order phase transitions, themselves delimited by multicritical points: Inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.

Global phase diagram of charge-neutral graphene in the quantum Hall regime for generic interactions

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunneling studies universally find Kekul\'e bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekul\'e order exists in the region of the phase diagram believed to correspond to real samples. In this work, starting from the continuum limit appropriate for experiments, we present the complete phase diagram of $\nu=0$ graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling), we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.

Dynamics of the restricted vortex problem with a honeycomb configuration

In this paper, we have investigated the restricted 14-vortex problem with a honeycomb configuration similar to the football surface pattern. First, we give a sufficient condition for the existence of honeycomb configurations and obtain the instability of configurations. Then, we establish the equation of motion of the tracer particle for the restricted 14-vortex problem and analyze the stability and distribution of equilibrium points and singular points. As can be seen from the global phase diagram of system, there are only four types of orbits: equilibrium points, homoclinic orbits, heteroclinic orbits, and periodic orbits.

Exploring interacting topological insulator in the extended Su-Schrieffer-Heeger model

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.

Nematic ordering in the Heisenberg spin-glass system in three dimensions.

Nematic ordering, where the spins globally align along a spontaneously chosen axis irrespective of direction, occurs in spin-glass systems of classical Heisenberg spins in d=3. In this system where the nearest-neighbor interactions are quenched randomly ferromagnetic or antiferromagnetic, instead of the locally randomly ordered spin-glass phase, the system orders globally as a nematic phase. This nematic ordering of the Heisenberg spin-glass system is dramatically different from the spin-glass ordering of the Ising spin-glass system. The system is solved exactly on a hierarchical lattice and, equivalently, Migdal-Kadanoff approximately on a cubic lattice. The global phase diagram is calculated, exhibiting this nematic phase, and ferromagnetic, antiferromagnetic, disordered phases. The nematic phase of the classical Heisenberg spin-glass system is also found in other dimensions d>2: We calculate nematic transition temperatures in 24 different dimensions in 2<d≤4.

Global phase diagram of bound states in the continuum

Bound states in the continuum (BICs) in photonic-crystal slabs have been conventionally classified into three types: single-resonance parametric, symmetry-protected, and Friedrich–Wintgen BICs. Here, we show that the single-resonance parametric BICs come from the coupling between the guided resonance (GR) and Fabry–Perot (FP) modes, and the symmetry-protected BICs from the coupling between degenerate GR modes. Hence, the three types of BICs in photonic-crystal slabs can be classified by the three different Friedrich–Wintgen origins. Based on this universal classification, a global phase diagram of BICs can be obtained with each phase identified by the indices of the three different Friedrich–Wintgen-type BICs. When BICs are created or annihilated, a phase transition occurs and is experimentally observed, in which the FP modes play a significant role. Our work shows a clear physical picture on whether BICs exist and how sensitive they are to changes in the parameter space, and enables improvements in experiment design and applications.

Disorder-induced phase transitions in double Weyl semimetals

The double Weyl semimetal (DWSM) is a newly proposed topological material that hosts Weyl points with chiral charge n=2. The disorder effect in DWSM is investigated by adopting the tight-binding Hamiltonian. Using the transfer matrix method and the noncommutative Kubo formula, we numerically calculate the localization length and the Hall conductivity in the presence of the on-site nonmagnetic disorder or orbital (spin-flip) disorders, and give the corresponding global phase diagrams. For the on-site nonmagnetic disorder, the system undergoes the DWSM-3D quantum anomalous hall (3D QAH) and normal insulator (NI)-DWSM phase transitions, and evolves into the diffusive metal (DM) phase before being localized by strong disorders, which is consistent with the Weyl semimetal. For \sigma_x orbital disorder, we find that increasing disorder can generate a pair of Weyl nodes at the boundary of the Brillouin zone and induce a 3D QAH-DWSM phase transition. Then we investigate the combined effect of orbital disorders for both disordered 3D QAH phase and DWSM phase. The disorder-induced transitions can be well understood in terms of an effective medium theory based on self-consistent Born approximation.

Dual-gated hBN/bilayer-graphene superlattices and the transitions between the insulating phases at the charge neutrality point

We report on transport properties in dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Here, BLG is nontwisted, i.e., plain. This paper focuses on the charge neutrality point (CNP) for a plain BLG. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected by varying a displacement field with the study on the resistance-temperature characteristics and the magnetoresistance. This work opens avenues for exploring the global phase diagram of the hBN/BLG superlattices beyond the CNP.