Geometrical Phase Transition Research Articles

Emergence of high-mass stars in complex fiber networks (EMERGE)

Context. Identified as parsec-size, gas clumps at the junction of multiple filaments, hub-filament systems (HFS) play a crucial role during the formation of young clusters and high-mass stars. These HFS still appear to be detached from most galactic filaments when compared in the mass–length (M–L) phase space. Aims. We aim to characterize the early evolution of HFS as part of the filamentary description of the interstellar medium (ISM). Methods. Combining previous scaling relations with new analytic calculations, we created a toy model to explore the different physical regimes described by the M–L diagram. Despite its simplicity, our model accurately reproduces several observational properties reported for filaments and HFS, such as their expected typical aspect ratio (A), mean surface density (Σ), and gas accretion rate (ṁ). Moreover, this model naturally explains the different mass and length regimes populated by filaments and HFS, respectively. Results. Our model predicts a dichotomy between filamentary (A ≥ 3) and spheroidal (A < 3) structures connected to the relative importance of their fragmentation, accretion, and collapse timescales. Individual filaments with low accretion rates are dominated by an efficient internal fragmentation. In contrast, the formation of compact HFS at the intersection of filaments triggers a geometric phase-transition, leading to the gravitational collapse of these structures at parsec-scales in ~1–2 Myr. In addition, this process also induces higher accretion rates.

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model

Free energy as a function of polarization is calculated for the square-lattice J_1J1-J_2J2 Ising model for J_2 < |J_1|/2J2<|J1|/2 using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at J_2 > |J_1|/4J2>|J1|/4. These findings enrich our knowledge of the J_1J1-J_2J2 Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.

Theoretical study of CDW phases for bulk NbX2 (X = S and Se).

In most two-dimensional transition metal chalcogenides, the superconducting phase coexists with the charge density wave (CDW) phase. There exists at least one case, i.e. bulk 2H-NbS2, that does not conform to this picture. Scientists have shown great interest in trying to experimentally find the CDW phase of bulk NbS2 since 1975. Is there any theoretically more stable thermodynamic state than its higher-temperature metal phase, especially in the case of charge injection? Theoretically more stable CDW bulk configurations (TC for 2H-NbS2 and TTs for 2H-NbSe2) with partial pseudo energy gaps were predicted through the harmonic phonon softening theory and first-principles calculations. The ratios of larger to smaller pseudo gaps around K-H segment in the Brillouin zone for CDW phases are basically equal to those of superconductivity phases for bulk 2H-NbX2 (X = S and Se). The CDW phase should coexist with its superconductor state below the critical temperature rather than the metal phase for bulk 2H-NbS2. The presence of CDW phase should be more easily observed experimentally when the injected charge reaches 0.5e/Nb18S36 for bulk 2H-NbS2. Our calculations of density of state (DOS) indicated that, during Nb atoms contracting to form the CDW phases with symmetry breaking in the in-plane direction, dominant conductive carriers are always of p-type for bulk 2H-NbS2 while the alternation of carrier type from p-type to n-type occurs for bulk 2H-NbSe2. The Fermi level continuously drops and then the M-L segment of the out-of-plane energy band emerges from the Fermi surface, which corresponds to the reversal of p-n type sign. Lifshitz transition of pocket-vanishing types occurs in the out-of-plane direction without symmetry breaking during the geometrical structural phase transition for bulk 2H-NbSe2. Our calculations have theoretically addressed the long-standing coexistence issue of CDW and superconducting phases.

Machine learning approach to percolation transitions: global information

Recently, a machine learning (ML) approach has been proposed to determine the percolation threshold and critical behaviors of percolation transitions (PTs), based on the ML algorithm used for the phase transition in thermal equilibrium systems. However, we have observed that the conventional ML approach used for thermal systems does not accurately provide the percolation threshold, in particular when the training regions for ML are asymmetrical with respect to its known value. Here, we remark that percolation is a geometric phase transition, and thus global information, rather than the local configurations used in thermal systems, is needed to determine the percolation threshold. To address this, we assign a parent node index to each node, which is updated during cluster merging, capturing global information on the ancestor of each node. Utilizing this quantity as input data for the convolutional neural network in the ML algorithm, we successfully obtain the correct percolation threshold regardless of whether the training regions are symmetric or asymmetric with respect to the known value. This validity holds independently of the PT type: continuous, hybrid, or discontinuous. As the concept of percolation is applied to various phenomena, this ML algorithm could be used ubiquitously.

Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd

Ising and Potts models can be studied using the Fortuin–Kasteleyn representation through the Edwards–Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h > 0. In this representation, which is also known as the random-cluster model, the Kertész line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in Zd. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kertész line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kertész line phase transition.

Nanoparticle geometrical effects on percolation, packing density, and magnetoresistive properties in ferromagnet-superconductor-insulator nanocomposites

The influence of nanoparticle geometrical and percolation effects on the electrical transport and magnetotransport properties of the system are investigated in a number of binary networks composed of superconducting (${\mathrm{MgB}}_{2}$), ferromagnetic (${\mathrm{CrO}}_{2}$ or ${\mathrm{La}}_{1/3}{\mathrm{Sr}}_{2/3}{\mathrm{MnO}}_{3}$), and insulating (${\mathrm{LiCoO}}_{2}$ or ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$) nanoparticles. For all-metal ${\mathrm{CrO}}_{2}/{\mathrm{MgB}}_{2}$ binary composites an anomalously high resistance state with two distinct percolation thresholds is found within a narrow range of the constituent composition, as a result of the strong suppression of heterointerfacial conductance between superconducting and half-metallic (${\mathrm{CrO}}_{2}$) nanoparticles and an unexpectedly large value of the percolation threshold of ${\mathrm{MgB}}_{2}$. The latter can be attributed to the geometric mismatch between the constituent nanoparticles and the related particle packing and excluded volume effects. The filling factor in this binary composite attains a maximum near the same percolation threshold and exhibits a power-law scaling behavior, which would indicate another geometric phase transition. The geometric effect of constituent particles is also verified through the large changes of percolation threshold in different types of combinations of binary components. Interestingly, the percolation transitions in these binary nanocomposites, either in the case of single or double percolation, are found to be governed by an unconventional scaling behavior of resistance just below the percolation threshold, due to mechanisms determined by heterogeneous interfaces of particles that are absent in conventional single-component percolation systems. In addition, magnetotransport is investigated in ${\mathrm{CrO}}_{2}/{\mathrm{MgB}}_{2}$ junctions, demonstrating nonhysteretic low-temperature magnetoresistance at the half-metal/Type II superconductor interface with the highest values around $42%$ at liquid helium temperatures obtained at volume fraction between the two percolation thresholds. The results show large variations of magnetoresistance that are highly sensitive to the constituent composition and the sample temperature near the percolation thresholds, demonstrating the interrelation between the structural or geometrical property of the system and materials functionality.

Adsorption of Metals on (100) Metallic Surfaces: Monte Carlo Simulations and Geometrical Phase Transitions.

Adsorption and continuous phase transitions (percolation) of metals on (100) metallic surfaces are studied by means of Monte Carlo simulations and the finite-size scaling theory. The studied systems are Ag/Au(100), Au/Ag(100), Ag/Pt(100), and Pt/Ag(100), and the embedded atom method (EAM) is employed for energy calculations. Pairwise interactions are also considered for comparative purposes. The study of critical exponents reveals that these systems belong to the same universality as random sequential adsorption (RSA). For the four systems studied, and the two kinds of interactions considered, phase diagrams of percolation threshold, θc, as a function of temperature are presented. In all cases, and for all temperatures, θc is always below the value corresponding to RSA, as expected for attractive interactions, and it tends to that value as T → ∞. At intermediate temperatures, a particular behavior is found for EAM interactions.

Observational assessment of the viability of de Sitter Gödel de Sitter phase transition

de Sitter--G\"odel--de Sitter phase transition(dGd) is a possible geometrical phase transition in the very early universe. It induces fluctuations with possibly observable traces on matter and radiation fields. Here we present a simulation based on dGd to investigate possible perturbations which could be along with the standard inflationary fluctuations in the cosmic microwave background (CMB) and distribution of the large-scale structure. The power spectrum of perturbations is characterized by a parameter pair, labeled here as ($p_1, p_2$). With {\it Planck} observations we find $p_1=0.008^{+0.003}_{-0.008}$ and $p_2= 0.002^{+0.001}_{-0.002}$ consistent with pure inflationary power spectrum and no hint for the dGd transition. Also, it is estimated future large-scale surveys such as Euclid and SKA can further tighten the constraints up to an order of magnitude and probe the physics of the early universe with much higher precision.

Analytical modeling and numerical analysis for tunable topological phase transition of flexural waves in active sandwiched phononic beam systems

Topological phononic crystals (PnCs) have attracted tremendous research attention in recent years. A significant hallmark of these structures is that these crystals can support interface modes that are robust to structural disturbance and protected by topology. In this study, we propose a new type of active sandwiched PnC beam for inducing topological geometric phase transition and topologically protected interface modes (TPIMs) for one-dimensional (1D) systems. The layered system comprises two commonly used active materials, i.e., barium titanate (BaTiO3) and cobalt ferric oxide (CoFe2O4). Analytical modeling for this layered system is derived in the framework of linearly constitutive relations of a magneto-electro-elastic (MEE) material with temperature effects. Two analytical approaches, i.e., the spectral element method (SEM) and the plane wave expansion (PWE) method, are applied to derive the theoretical band structure of the system and excellent agreement is reported. A numerical analysis based on the finite element method (FEM) is adopted for further validation. The influence of outer fields in the bandgap frequency is examined and the size-dependent properties are also analyzed. Moreover, the transmission response is determined via analytical modeling and numerical analysis. It is found that the robust TPIMs are immune to defects and disorders. Conclusively, this study puts forward a new type of beam system for inducing topological phase transition. It can be readily extended to more complex systems and higher-order models.

Nonlinear Vibration Isolation via a NiTiNOL Wire Rope

Vibration isolators with both stiffness and damping nonlinearities show promise for exhibiting compound advantages for broadband vibration isolation. A nonlinear isolator with a NiTiNOL wire rope is proposed with cubic stiffness, hysteretic damping, and pinching effects induced by geometric constraints, inner frictions, and phase transitions, respectively. A combined method of a beam constraint model and a Bouc-Wen model is presented to characterize the restoring force of the NiTiNOL wire rope. The frequency responses of the nonlinear isolator were analyzed through a harmonic balance method with an alternating frequency/time domain technique. The generalized equivalent stiffness and the generalized equivalent damping ratio were defined for a comprehensive understanding of the nonlinear characteristics. The isolator exhibited a stiffness-softening-hardening characteristic. The pinching effect, the Bouc-Wen hysteresis, and the cubic stiffness mainly influenced the equivalent stiffness at the initial value, the small displacements, and the large displacements, respectively. The rate-independent damping ratio increased and then decreased with increasing displacement, and the parameters influenced the damping ratio change in different ways. Compared to an isolator with a steel wire rope, the isolator with a NiTiNOL wire rope exhibited less initial stiffness and a stronger damping effect, and thus, better vibration isolation performance. The relationships of the peak displacement transmissibility and the resonant frequency with the excitation amplitude were both non-monotonic due to the non-monotonic changes of the stiffness and the damping ratio. The minimum peak transmissibility, the lowest resonant frequency, and their corresponding excitation amplitudes depended on the isolator parameters. The isolator demonstrated stiffness–softening and stiffness–hardening types of jump phenomena with different parameters.

Aspects of a Phase Transition in High-Dimensional Random Geometry.

A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short-selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields, and offer the possibility for further ramifications.

Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find an excellent agreement between them for large sizes of the system in a wide region of the parameter space, except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.

Resistance fluctuations in superconducting K x Fe2 – y Se2 single crystals studied by low-frequency noise spectroscopy* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11774303 and 11574373) and Joint Fund of Yunnan Provincial Science and Technology Department, China (Grant No. 2019FY003008).

Low-frequency resistance noise spectroscopy is applied to investigate bulk single crystals of the intercalated iron-selenide K x Fe2 – y Se2 superconductors with different iron vacancy orders. Based on a generalized fluctuation model, the well-observed resistance hump above 100 K is interpreted as an insulator–metal phase transition with a characteristic transition energy of 0.1–0.6 eV, indicating a highly inhomogeneous energy distribution configuration. In the superconducting transition regime, we find that the normalized resistance noise scales with resistance R excellently as SR /R 2 ∝ R l rs with the noise exponent l rs ≈ 1.4. With reduced iron vacancy disordering in enhanced superconductivity K x Fe2 – y Se2 crystals, the level of resistance fluctuations is greatly suppressed, suggesting a geometrical phase transition for conduction channel, which is directly related to the microstructure of the crystals.

Multiscale Charge Transport in van der Waals Thin Films: Reduced Graphene Oxide as a Case Study.

Large area van der Waals (vdW) thin films are assembled materials consisting of a network of randomly stacked nanosheets. The multiscale structure and the two-dimensional (2D) nature of the building block mean that interfaces naturally play a crucial role in the charge transport of such thin films. While single or few stacked nanosheets (i.e., vdW heterostructures) have been the subject of intensive works, little is known about how charges travel through multilayered, more disordered networks. Here, we report a comprehensive study of a prototypical system given by networks of randomly stacked reduced graphene oxide 2D nanosheets, whose chemical and geometrical properties can be controlled independently, permitting to explore percolated networks ranging from a single nanosheet to some billions with room-temperature resistivity spanning from 10-5 to 10-1 Ω·m. We systematically observe a clear transition between two different regimes at a critical temperature T*: Efros-Shklovskii variable-range hopping (ES-VRH) below T* and power law behavior above. First, we demonstrate that the two regimes are strongly correlated with each other, both depending on the charge localization length ξ, calculated by the ES-VRH model, which corresponds to the characteristic size of overlapping sp2 domains belonging to different nanosheets. Thus, we propose a microscopic model describing the charge transport as a geometrical phase transition, given by the metal-insulator transition associated with the percolation of quasi-one-dimensional nanofillers with length ξ, showing that the charge transport behavior of the networks is valid for all geometries and defects of the nanosheets, ultimately suggesting a generalized description on vdW and disordered thin films.

Stability analysis of an ensemble of simple harmonic oscillators

In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to variations of the parameters, viz. the mass, temperature and the frequency of oscillators. Here, we introduce the Hessian matrix of the partition function as the model embedding function from the space of parameters to the set of real numbers. In this framework, we classify the regions in the parameter space of the harmonic oscillator fluctuations where they yield a stable statistical configuration. The mechanism of stability follows from the notion of the fluctuation theory. In Secs. 7 and 8, we provide the nature of local and global correlations and stability regions where the system yields a stable or unstable statistical basis, or it undergoes into geometric phase transitions. Finally, in Sec. 9, the comparison of results is provided with reference to other existing research.

Deterministic interface modes in two-dimensional acoustic systems

The interface state in two-dimensional (2D) sonic crystals (SCs) was obtained based on trying or cutting approach, which greatly limits its practical applications. In this paper, we theoretically demonstrate that one category of interface states can deterministically exist at the boundary of two square-lattice SCs due to the geometric phase transitions of bulk bands. First, we derive a tight-binding formalism for acoustic waves and introduce it into the 2D case. Furthermore, the extended 2D Zak phase is employed to characterize the topological phase transitions of bulk bands. Moreover, the topological interface states can be deterministically found in the nontrivial bandgap. Finally, two kinds of SCs with the [Formula: see text] symmetry closely resembling the 2D Su–Schrieffer–Heeger (SSH) model are proposed to realize the deterministic interface states. We find that tuning the strength of intermolecular coupling by contacting or expanding the scatterers can effectively induce the bulk band inversion between the trivial and nontrivial crystals. The presence of acoustic interface states for both cases is further demonstrated. These deterministic interface states in 2D acoustic systems will be a great candidate for future waveguide applications.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

Decoding a Percolation Phase Transition of Water at ∼330 K with a Nanoparticle Ruler.

Liquid water, despite its simple molecular structure, remains one of the most fascinating and complex substances. Most notably, many questions continue to exist regarding the phase transitions and anomalous properties of water, which are subtle to observe experimentally. Here, we report a sharp transition in water at 330 K unveiled through experimental measurements of the instantaneous Brownian velocity of NaYF4:Yb/Er upconversion nanoparticles in water. Our experimental investigations, corroborated by molecular dynamics simulations, elucidate a geometrical phase transition where a low-density liquid (LDL) clusters become percolated below 330 K. Around this critical temperature, we find the sizes of the LDL clusters to be similar to those of the nanoparticles, confirming the role of the upconversion nanoparticle as a powerful ruler for measuring the extensiveness of the LDL hydrogen-bond network and nanometer-scale spatial changes (20-100 nm) in liquids. Additionally, a new order parameter that unequivocally classifies water molecules into two local geometric states is introduced, providing a new tool for understanding and modeling water's many anomalous properties and phase transitions.

Analytical and Numerical Solution of the Problem on Brachistochrones in some General Cases

In this paper, we discuss J. Bernoulli’s brachistochrone problem and find its analytical and numerical solutions in the cases where viscous or dry friction are taken into account. We predict the existence of a point of “geometrical phase transition” u0 = ln(1/2k2b); it corresponds to the transition from one class of trajectories to another that qualitatively differs from the initial class. Numerical simulation of the motion in a neighborhood of points of geometric phase transitions is performed. We prove that in the absence of friction forces, the minimization problem for the motion time for any motion along a curvilinear trough under the action of the gravity force can always be reduced to the brachistochrone problem and can be solved without involving methods of calculus of variation, only by general dynamical laws. We find a solution to the classical Bernoulli problem under the condition that the length of the trajectory is fixed. We show that under this isoperimetric condition, the class of trajectories differs from the classical brachistochrone. We also observe the transformation of these trajectories to the cycloid by numerical and analytical analysis.