Higher-order Phase Transition Research Articles

A research of higher-order network emotional phase transitions

This paper explores the law of emotion transmission on the social Internet. By applying higher-order network theory, ER random networks are reconstructed and higher-order network structures with multiple interaction points are generated. The I-state of the SI model is extended to set up the propagation rules of emotions based on higher-order networks. Concepts such as sentiment recession rate are introduced to make sentiment propagate through different simplexes, so as to obtain the propagation rules of higher-order networks. Qualitative analysis of emotional changes during the propagation process verifies the phase transition phenomenon of emotions in the network. By comparing simulated results with actual data, we demonstrate the accuracy of our higher-order network-based emotion propagation model in reflecting real-world trends and outcomes. The study also explores the effects of factors such as the initial proportion of extreme emotions on emotion propagation. This study provides valuable insights into understanding the operation of complex systems and offers important implications for government predictions of opinion development.

Detecting phase transitions in lattice gauge theories: Production and dissolution of topological defects in 4D compact electrodynamics

We present the application of microcanonical inflection point analysis (MIPA)—a novel and powerful method for the systematic identification and classification of phase transitions (PTs)—to the microcanonical formulation of lattice gauge theories. Specifically, we explore how this approach sheds light on collective phenomena such as the emergence of topological order in quantum field theories. As a case study, we show how to systematically characterize PTs in 4D U(1) lattice electrodynamics. Beyond identifying the well-established deconfinement PT (DPT) associated with pair dissolution, classified as a first-order PT, we uncover two higher-order PTs not observed before. Thanks to the application of the MIPA, we identify an independent third-order PT in the confined phase and indications of a dependent third-order PT in the deconfined (Coulomb) phase. To gain physical insights into these PTs, we numerically compute the average number density of monopolar and pair defects as a function of energy. Notably, our findings reveal that the pair dissolution mechanism extends beyond a singular transitional phenomenon coinciding with the DPT. Instead, it encompasses a spectrum of transitional phenomena, as indicated by the rates of acceleration and deceleration in the dissolution of pairs as a function of energy. Finally, we briefly discuss how such a method can be extended to more complex quantum field theories on a lattice. Published by the American Physical Society 2024

Statistical modeling of equilibrium phase transition in confined fluids

The phase transition of confined fluids in mesoporous materials deviates from that of bulk fluids due to the interactions with the surrounding heterogeneous structure. For example, adsorbed fluids in metal-organic-frameworks (MOFs) have atypical phase characteristics such as capillary condensation and higher-order phase transitions due to a strong heterogeneous field. Considering a many-body problem in the presence of a nonuniform external field, we model the host-guest and guest-guest interactions in MOFs. To solve the three-dimensional Ising model, we use the mean-field theory to approximate the guest-guest interactions and Mayer's f-functions to describe the host-guest interactions in a unit cell. Later, using Hill's theory of nanothermodynamics, we define differential thermodynamic functions to understand the distribution of intensive properties and integral thermodynamic functions to explain the phase transition in confined fluids. The investigation reveals a distinct behavior where fluids confined in larger pores undergo a discontinuous (first-order) phase transition, whereas those confined in smaller pores experience a continuous (higher-order) phase transition. Furthermore, it is observed that the free-energy barrier for low-density adsorbed fluid (LDAF) to high-density adsorbed fluid (HDAF) phase transitions is lower in confined fluids than in bulk fluids resulting in a lower condensation pressure relative to the bulk saturation pressure. Finally, the integral thermodynamic functions are succinctly presented in the form of a phase diagram, marking an initial step toward a more practical approach for understanding the phase behavior of confined fluids. Published by the American Physical Society 2024

Delocalization and higher-order topology in a nonlinear elastic lattice

Topological elastic waves provide novel and robust ways for manipulating mechanical energy transfer and information transmission, with potential applications in vibration control, analog computation, and more. Recently discovered higher-order topological insulators (HOTIs) with multidimensional and hierarchical edge states can further expand the capabilities of topological elastic waves. However, the effects of nonlinearity on elastic HOTIs remain elusive. In this paper, we propose a nonlinear elastic higher-order topological Kagome lattice. After briefly reviewing its linear properties, we explore the effects of nonlinearity on the higher-order band topology and topological states. To do this, we have developed a method to calculate approximate nonlinear modes in order to identify the bulk polarization and probe the higher-order topological phase in the nonlinear lattice. We find that nonlinearity induces unusual delocalization of topological corner states, band crossing, and higher-order topological phase transition. The delocalization reveals that intracell hardening nonlinearity leads to direct delocalization of topological corner states while intracell softening nonlinearity first enhances and then reduces localization. The nonlinear higher-order topological phase is amplitude dependent, and we demonstrate a transition from a trivial to a non-trivial phase, enabling amplitude induced topological corner and edge states. Additionally, this phase transition corresponds to the closing and reopening of the bandgap, accompanied by an unusual band crossing. By examining the band topology before and after the band crossing, we find that the bulk polarization becomes quantized with respect to amplitude and can predict higher-order topological phases in nonlinear lattices. The obtained results are expected to be beneficial for the development of tunable and robust elastic wave devices.

Calorimetric, optical and dielectric measurements on two Schiff's based liquid crystalline materials exhibiting multiple phase transitions.

We report high-resolution calorimetric, optical and dielectric studies on two Schiff's based liquid crystalline materials, 4O.5 and 5O.5, which exhibit multiple phase transitions. The study goes beyond the commonly studied isotropic-to-nematic (I-N) and nematic-to-smectic A (N-SmA) phase transitions and explores higher-order smectic phase transitions. The critical exponent, α values, for different phase transitions has been explored. For the I-N, N-SmA, SmA-SmC, SmC-SmF, SmF-CrG and SmB-CrG transitions, α values close to 0.5 and amplitude ratios A-/A+ ~ 1.6 and D-/D+ ~ 1 indicate a first-order nature. Notably, for the SmA-SmB transition, although α (≈ 0.64) is larger than the tricritical value of 0.5, A-/A+ ~ 1.2 and D-/D+ ~ 1, and the study reports an order parameter critical exponent (β) of 0.26 ± 0.002, which supports a tricritical nature for this transition. Importantly, the ratios of A-/A+ and D-/D+ are found to have similar values across all three-measurement methods, indicating consistency and agreement among these methods.

LIGO-Virgo constraints on dark matter and leptogenesis triggered by a first order phase transition at high scale

We study the possibility of constraining a scenario with high scale first order phase transition (FOPT) responsible for the cogenesis of baryon and dark matter using gravitational wave (GW) (non)observations. While the FOPT at high scale is responsible for generating baryon asymmetry through leptogenesis and dark matter via the mechanism, the resulting GW spectrum falls within the ongoing LIGO-Virgo experimental sensitivity. The dark matter is preferred to be in the nonthermal ballpark with sub-GeV masses and the criteria of successful dark matter relic rules out a large portion of the parameter space consistent with high scale FOPT and successful leptogenesis. Some part of the parameter space allowed from dark matter and leptogenesis criteria also gives rise to a large signal-to-noise ratio at ongoing experiments and hence can be disfavored in a conservative way from the nonobservation of such stochastic GW background. Future data from ongoing and planned experiments will offer a complementary and indirect probe of the remaining parameter space which is typically outside the reach of any direct experimental probe. Published by the American Physical Society 2024

Holding water in a sieve—stable droplets without surface tension

Our understanding of supercritical fluids has seen exciting advances over the last decades, often in direct contradiction to established textbook knowledge. Rather than being structureless, we now know that distinct supercritical liquid and gaseous states can be distinguished and that a higher order phase transition - pseudo boiling - occurs between supercritical liquid and gaseous states across the Widom line. Observed droplets and sharp interfaces at supercritical pressures are interpreted as evidence of surface tension due to phase equilibria in mixtures, given the lack of a supercritical liquid-vapor phase equilibrium in pure fluids. However, here we introduce an alternative physical mechanism that unexpectedly causes a sharpening of interfacial density gradients in absence of surface tension: thermal gradient induced interfaces (TGIIF). We show from first principles and simulations that, unlike in gases or liquids, stable droplets, bubbles, and planar interfaces can exist without surface tension. These results challenge and generalize our understanding of what droplets and phase interfaces are, and uncover yet another unexpected behavior of supercritical fluids. TGIIF provide a new physical mechanism that could be used to tailor and optimize fuel injection or heat transfer processes in high-pressure power systems.

Unified characterization for higher-order topological phase transitions

Unified characterization for higher-order topological phase transitions

Corner states in photonic higher-order Dirac semimetals

The introduction of higher-order topological insulators featuring topological corner states has been an extremely active topic for the generation of confined modes. Recent studies show that corner states are not an exclusive feature of topological insulators but can also exist as bound states in the continuum (BIC). This suggests that corner states may exist in different topological phases that exhibit a higher-order character, beyond the conventional bulk-edge correspondence. In this paper, we show that corner states can appear in a higher-order Dirac semimetal phase of a two-dimensional photonic lattice. Such a lattice displays a dispersion relationship with a fourfold degeneracy, which serves to induce a higher-order topological phase transition, leaving a Dirac point between two edge bands. Just as Dirac modes exist in regular lattice defects, the nonconventional bulk-edge-corner correspondence leads to corner states in the Dirac semimetal phase. Notably, the induced corner state exhibits an algebraic decay characteristic of long-range interactions, predicted by the massless Dirac equation. The analysis of the field profile and quality factors indicates that the state is not a BIC, but rather a corner-Dirac state. We show that if the photonic lattice does not present a higher-order phase transition the existence of the corner-Dirac state does not arise. The results obtained in this paper indicate that corner states can exist throughout the entire topological phase transition process, even in the semimetal phase, and pave the way to generate light-matter interactions with such a photonic bath.

Fracton critical point at a higher-order topological phase transition

The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. Here we demonstrate that the existence of a two-dimensional topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find that the QCP is characterized by a critical dipole liquid theory with subsystem U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $Lln(L)$. Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\ensuremath{\omega}={k}_{x}{k}_{y}.$

Density-driven higher-order topological phase transitions in amorphous solids

Amorphous topological states, which are independent of the specific spatial distribution of microscopic constructions, have gained much attention. Recently, higher-order topological insulators, which are a new class of topological phases of matter, have been proposed in amorphous systems. Here, we propose a density-driven higher-order topological phase transition in a two-dimensional amorphous system. We demonstrate that the amorphous system hosts a topological trivial phase at low density. With an increase in the density of lattice sites, the topological trivial phase converts to a higher-order topological phase characterized by a quantized quadrupole moment and the existence of topological corner states. Furthermore, we confirm that the density-driven higher-order topological phase transition is size dependent. In addition, our results should be general and equally applicable to three-dimensional amorphous systems. Our findings may greatly enrich the study of higher-order topological states in amorphous systems.

Pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices

This article offers a detailed analysis of pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices. We carry out Wang–Landau sampling to obtain the density of states. Using microcanonical inflection-point analysis with microcanonical entropy, we obtain the order of the pseudo-phase transitions in the models. The microcanonical analysis results of the second-order transition for the Ising model and the first-order transition for the Baxter–Wu model are consistent with the traditional canonical results. In addition, the third-order transitions are found in both models, implying the universality of higher-order phase transitions.

Circuit quantum electrodynamics simulator of the two-dimensional Su-Schrieffer-Heeger model: higher-order topological phase transition induced by a continuously varying magnetic field.

Higher-order topological insulator (HOTI) occupies an important position in topological band theory due to its exotic bulk-edge correspondence. Recently, it has been predicted that external magnetic field can induce novel topological phases in 2D HOTIs. However, up to now the theoretical description is still incomplete and the experimental realization is still lacking. Here we proposed a superconducting quantum circuit simulator of 2D Su-Schriffer-Heeger lattice, which is one of the most celebrated HOTI models, and investigate consequently the influence of the continuously varying magnetic field. By using the parametric conversion coupling method, we can establish in principle the time- and site-resolved tunable hopping constants in the proposed architecture, thus providing an ideal platform for investigating the higher-order topological phase transitions induced by continuously varying magnetic field. Our numerical calculation further shows that the higher-order topology of the lattice, which manifests itself through the existence of the zero energy corner modes, exhibit exotic and rich dependence on the imposed magnetic field and the inhomogeneous hopping strength. To probe the proposed magnetic-field-induced topological phase transition, we study the response of the lattice to the corner site pumping in the steady state limit, with results implying that the predicted topological phase boundaries can be unambiguously identified by the measurement of the corner sites and their few neighbors. Requiring only current level of technology, our scheme can be readily tested in experiment and may pave an alternative way towards the future investigation of HOTIs under various mechanisms including magnetic field, disorder, and strong correlation.

Self-organized quantization and oscillations on continuous fixed-energy sandpiles.

Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboardlike spatiotemporal organization. We study a simple model for local activation-inhibition processes. Our model, first introduced in the context of atmospheric moisture dynamics, is a continuous-energy and non-Abelian version of the fixed-energy sandpile model. Each lattice site is populated by a nonnegative real number, its energy. Upon each timestep all sites with energy exceeding a unit threshold redistribute their energy at equal parts to their nearest neighbors. The limit cycle dynamics gives rise to a complex phase diagram in dependence on the mean energy μ: For low μ, all dynamics ceases after few redistribution events. For large μ, the dynamics is well-described as a diffusion process, where the order parameter, spatial variance σ, is removed. States at intermediate μ are dominated by checkerboardlike period-two phases which are however interspersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in σ or ∂_{μ}σ-akin to first- and higher-order phase transitions. Overall, the energy landscape is dominated by few energy levels which occur as sharp spikes in the single-site density of states and are robust to noise.

Microstructural and thermodynamic study of γ-Ga2O3

Abstract The metastable nanocrystalline γ form of gallium oxide has been prepared and its microstructure and thermochemistry have been studied for the first time by employing X-ray and electron diffraction, high-resolution transmission electron microscopy, adiabatic and differential scanning calorimetry. The randomly oriented crystallites of maximum 5 nm in size have been observed. The sponge-like morphology of γ-Ga2O3 particles may explain the high specific surface area, previously reported for this material. The defect spinel-type structure of γ-Ga2O3 is similar to that of γ and η-Al2O3. Up to 5.7 wt.% of water can be stored in γ-Ga2O3 and subsequently released at elevated temperatures. Dry γ-Ga2O3 specifically absorbs atmospheric water at room temperature. The transformation of γ-Ga2O3 into stable β-Ga2O3 occurs in two steps. In the range 650–800 K, γ'-Ga2O3 is formed in the course of a reversible higher-order phase transition. The latter irreversibly transforms into β-form above 873 K. The enthalpy of this exothermic transformation is determined as –19.3 ± 0.4 kJ · mol–1. The coefficients of the Gibbs energy equation for γ and γ'-Ga2O3 have been assessed.

Direct dynamical characterization of higher-order topological phases with nested band inversion surfaces

Higher-order topological phases (HOTPs) are systems with topologically protected in-gap boundary states localized at their (d-n)-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the so-called band inversion surfaces (BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra (a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.

CDT Quantum Toroidal Spacetimes: An Overview

Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace’s equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. When such scalar fields are included as dynamical fields in the path integral, they can have a dramatic effect on the geometry.

The higher-order phase transition in toroidal CDT

We investigate the transition between the phases B and Cb observed in four-dimensional Causal Dynamical Triangulations (CDT). We find that the critical properties of CDT with toroidal spatial topology are the same as earlier observed in spherical spatial topology where the B − Cb transition was found to be higher-order. This may have important consequences for the existence of the continuum limit of CDT, describing the perspective UV limit of quantum gravity, which potentially can be investigated in the toroidal model.

Local-Basis-Function Equation of State for Ice VII–X to 450 GPa at 300 K

Helmholtz energy of ice VII–X is determined in a pressure regime extending to 450 GPa at 300 K using local-basis-functions in the form of b-splines. The new representation for the equation of state is embedded in a physics-based inverse theory framework of parameter estimation. Selected pressures as a function of volume from 14 prior experimental studies and two theoretical studies constrain the behavior of Helmholtz energy. Separately measured bulk moduli, not used to construct the representation, are accurately replicated below about 20 GPa and above 60 GPa. In the intermediate range of pressure, the experimentally determined moduli are larger and have greater scatter than values predicted using the Helmholtz representation. Although systematic error in the determination of elastic moduli is possible and likely, the alternative hypothesis is a slow relaxation time associated with changes in proton mobility or the ice VII to X transition. A correlation is observed between anomalies in the pressure derivative of the predicted bulk modulus and previously suggested higher-order phase transitions. Improved determinations of elastic properties at high pressure would allow refinement of the current equation of state. More generally, the current method of data assimilation is broadly applicable to other materials in high-pressure studies and for investigations of planetary interiors.

Staircase to higher-order topological phase transitions

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairing interaction, which is parametrized by an algebraic decay with exponent $\ensuremath{\alpha}$. Remarkably, in the limit $\ensuremath{\alpha}=1$ the order of the topological transition becomes infinite. We compute the critical exponents for the series of higher-order transitions in exact form and find that they fulfill the hyperscaling relation. We also study the critical behavior at the boundary of the system and discuss potential experimental platforms of magnetic atoms in superconductors.