Bulk Critical Point Research Articles

Measuring the Boundary Gapless State and Criticality via Disorder Operator.

The disorder operator is often designed to reveal the conformal field theory (CFT) information in quantum many-body systems. By using large-scale quantum MonteCarlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but it keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)_{1} CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.

Non-Hermitian extended midgap states and bound states in the continuum

We investigate anomalous localization phenomena in non-Hermitian systems by solving a class of generalized Su–Schrieffer–Heeger/Rice–Mele models and by relating their provenance to fundamental notions of topology, symmetry-breaking, and biorthogonality. We find two types of bound states in the continuum, both stable even in the absence of chiral symmetry: the first being skin bulk states, which are protected by the spectral winding number. The second type is constituted by boundary modes associated with a quantized biorthogonal polarization. Furthermore, we find an extended state stemming from the boundary state that delocalizes while remaining in the gap at bulk critical points. This state may also delocalize within a continuum of localized (skin) states. These results clarify fundamental aspects of topology and symmetry in light of different approaches to the anomalous non-Hermitian bulk-boundary correspondence and are of direct experimental relevance for mechanical, electrical, and photonic systems.

Photoreflectance spectroscopy of BiOCl epitaxial thin films

We have observed a new optical transition in the photoreflectance spectra of indirect-gap BiOCl thin films, which were grown on SrTiO3 substrates. The position of this transition is close in energy to its bulk critical point (CP) energy. Moreover, these are significantly lower than a higher-lying direct-type CP from an energetic point of view. The spectral line shape analysis for our observed signal suggests the presence of an excitonic effect of this compound. We determined its dependence of the optical anomaly on temperature ranging from 80 K to RT. We adopted the Varshni model for this analysis. At last, we compared photonic properties of BiOCl with those of an element and binary semiconductors.

Special transition and extraordinary phase on the surface of a two-dimensional quantum Heisenberg antiferromagnet

Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, y_{s}=0.86(4)ys=0.86(4) and \eta_{\parallel}=-0.33(1)η∥=−0.33(1), which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.

Phase lines in mean-field models with nonuniform external forces

We look at the influence of external fields on systems described by generic free energy functional of the order parameter. The external force may have arbitrary spatial dependence, and the order parameter coupling may be nonlinear. The treatment generalizes seemingly disparate works, such as pure fluids, liquid and polymer mixtures, lipid monolayers, and colloidal suspensions in electric fields, fluids, and nematics in gravity, solutions in an ultracentrifuge, and liquid mixtures in laser radiation. The phase lines and thermodynamic behavior are calculated at the mean-field level. We find a "surface" critical point that can be shifted to higher or lower temperatures than the bulk critical point. Below this point, the transition from a "gas" phase to a "liquid" phase is first-order, while above it, the transition is second-order. The second-order line is affected by the spatial dependence of the force, while the first-order line is universal. Moreover, the susceptibility may diverge at a finite location r. Several analytical expressions are given in the limit where a Landau expansion of the free energy is valid.

Quantum extraordinary-log universality of boundary critical behavior

The recent discovery of extraordinary-log universality has generated intense interest in classical and quantum boundary critical phenomena. Despite tremendous efforts, the existence of quantum extraordinary-log universality remains extremely controversial. Here, by utilizing quantum Monte Carlo simulations, we study the quantum edge criticality of a two-dimensional Bose-Hubbard model featuring emergent bulk criticality. On top of an insulating bulk, the open edges experience a Kosterlitz-Thouless-like transition into the superfluid phase when the hopping strength is sufficiently enhanced on edges. At the bulk critical point, the open edges exhibit the special, ordinary, and extraordinary critical phases. In the extraordinary phase, logarithms are involved in the finite-size scaling of two-point correlation and superfluid stiffness, which admit a classical-quantum correspondence for the extraordinary-log universality. Thanks to modern quantum emulators for interacting bosons in lattices, the edge critical phases might be realized in experiments.

Surface critical properties of the three-dimensional clock model

Surface effects are significant at the bulk critical point due to divergence of the correlation length. Recently, a novel extraordinary-log surface critical behavior was proposed in a 3D O($N$) model. Here, the authors study the surface properties of the 3D $q$-state clock model, where the ${Z}_{q}$ anisotropy is a prototype of dangerously irrelevant perturbation. They identify the existence of an extraordinary-log phase between ordinary and extraordinary phases at the bulk critical point as the consequence of the emergent O(2) symmetry.

Surface criticality of the antiferromagnetic Potts model

We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780(3)$, $\eta_\parallel=1.44(1)$, and $\eta_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $\eta_\parallel=-0.391(4)$, and $\eta_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $\eta_\perp=-0.442(5)$. If the ferromagnetic next nearest neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $\eta_\parallel=-0.69(1)$ and $\eta_\perp=-0.37(1)$, respectively.

Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field.

We study the nonequilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

Boundary criticality of the O(N) model in d = 3 critically revisited

It is known that the classical O(N)O(N) model in dimension d > 3dgt;3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. For the ordinary transition the bulk and the boundary order simultaneously; the extra-ordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3d=3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3d=3 and N \ge 2N≥2. Here we show that formally treating NN as a continuous parameter, there exists a critical value N_c > 2Ncgt;2 separating two distinct regimes. For 2 \leq N < N_c2≤N<Nc the extra-ordinary fixed point survives in d = 3d=3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of \log rlogr. For N > N_cNgt;Nc there is no fixed point with order parameter correlations decaying slower than power law. We discuss several scenarios for the evolution of the phase diagram past N = N_cN=Nc. Our findings appear to be consistent with recent Monte Carlo studies of classical models with N = 2N=2 and N = 3N=3. We also compare our results to numerical studies of boundary criticality in 2+1D quantum spin models.

Critical Depletion, Adsorption, and Intersurface Interaction in Polymer Solutions: A Mean-Field Theory Study

Using a self-consistent field theory, we examine the thermodynamics and interfacial properties of a homopolymer solution, either close to a single hard surface or confined between two parallel surfaces, in equilibrium with a bulk reservoir. We focus on the bulk critical regime and find that various physical quantities therein exhibit qualitatively different behaviors from those in the off-critical regime. For the single-surface system, the surface-excess Γ diverges as ln|ϕb – ϕc| and ln|χc – χ| when approaching the bulk critical point, where χ and ϕb are the Flory–Huggins interaction parameter and the volume fraction of polymer segment in bulk solution, respectively, and χc and ϕc are their respective values at the critical point. Γ diverges to +∞ when the surface–polymer interaction eₛ is larger than the depletion–adsorption transition (DAT) point ec, and to −∞ when eₛ < ec. As such, the DAT at ec in the critical regime is rather sharp and ec = 0.1824 + 0.1359N–¹/² at large N. For the two-surface system, the intersurface potential W at the critical point is purely attractive for both depleted and adsorbed cases and follows a D–³ power-law decay at large intersurface separations D; when eₛ is close to ec, the strength of W becomes rather weak. This nonmonotonic dependence of W on eₛ has important experimental implications on the stability of colloidal suspensions.

Surface critical behavior of coupled Haldane chains

The special surface transition at (2+1)-dimensional quantum critical point is precluded in corresponding classical critical point. The mechanism of such behavior which is only found in dimerized Heisenberg models so far is still under debate. To illuminate the role of symmetry protected topological (SPT) phase in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisted by interacting spin-1 Haldane chains, which has a genuine SPT phase--the Haldane phase--at weak interchain interactions and a quantum critical point belonging to the classical 3D O(3) universality class to the N\'eel phase. Different from models studied previously, there is no dimerization in the current model. Cutting the system along the chain direction or perpendicular to the chain direction exposes two different surfaces. Using unbiased quantum Monte Carlo simulations, we find that the two different types of surface show completely different surface critical behaviors at the bulk critical point, resulted from different surface states in the SPT phase. For the system with surfaces along the chain direction, the surface critical behavior is of ordinary type of the bulk 3D O(3) critical point, while for the surfaces perpendicular to the chain direction, the surface critical behavior is nonordinary, consistent with special transitions found in dimerized Heisenberg models. Our numerical results demonstrate that the gapless surface state in the gapped SPT phase together with the gapless mode of critical point is a pure quantum scenario that leads to the nonordinary transition.

Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement

To predict phase behavior of a pure component in nanopores, various versions of Kelvin equations and equation-of-state-with-capillary-pressure (EOS–Pcap) models have been used. There has been debate on the validity of Kelvin equation, especially in sub-10-nm pores. For EOS–Pcap models, numerical iterations have been used to obtain vapor–liquid equilibrium (VLE). In slit pores with widths larger than 8 nm, the Kelvin equation agrees with (within 10%) the equilibrium vapor-phase pressures of confined propane from engineering density functional theory between 310 K and 360 K. We introduce a graphical method using pressure–volume, chemical-potential–density, and chemical-potential–pressure relations to obtain VLE using EOS–Pcap model. While the Kelvin equation takes only surface tension as an input and returns a solution for VLE up until the bulk critical point (CP), the EOS–Pcap model predicts a limiting temperature different from the bulk CP. The predictions from Kelvin equations and EOS-Pcap models can be improved by considering adsorption layer thickness.

Interplay between Wetting and Filling of Argon Adsorption in Slit Pores with Different Surface Energies Transition from Filling in Micropores to Capillary Condensation in Mesopores

The concept of was first introduced by Dubinin (Dubinin, A. M. M. Q. Rev., Chem. Soc. 1955, 9, 101; Bering, B. P.; Dubinin, A. M. M.; Serpinsky, V. V. J. Colloid Interface Sci. 1966, 21, 378) to describe the adsorption in pores having widths of less than 1.5 nm at temperatures less than the bulk critical point temperature. In mesopores, another phenomenon, capillary condensation to a liquidlike adsorbate, or condensate, occurs (Do, D. D. Adsorption Analysis: Equilibria and Kinetics; World Scientific: London, 1983). The distinction between micropore filling and capillary condensation is not unambiguous. It is implicitly assumed in the literature that there is a strong attraction between the adsorbent and a given adsorbate, resulting in the formation of an adsorbed film which thickens as pressure increases. As the pressure approaches the bulk coexistence pressure, the adsorbed film on a planar surface becomes infinitely thick, a feature known as (complete) wetting. In this work, we provide a clear distinction between filling and condensation and also show how wetting behavior (nonwetting/partial wetting/continuous wetting) affects filling and condensation in slit pores and determine conditions under which filling occurs even when the surfaces are nonwetting or partial wetting. We have carried out extensive simulations of argon adsorption in slit pores to investigate the effects of substrate strength, pore size, and temperature on the transition from nonfilling to filling and condensation. From the analysis of the simulation results, we define filling as the phenomenon whereby a pore is filled before the formation of an adsorbate layer on the surface and capillary condensation as one in which adsorbate layers are formed on the pore walls prior to condensation. A parametric map or phase diagram of wetting/filling is constructed to show the interplay between the adsorbent strength, temperature, and pore size, which delineates the various regions of filling and capillary condensation.

A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids

Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry, and materials science. Progress has been hampered by the lack of a comprehensive and unified understanding of the physics of wetting and drying phase transitions. Using various theoretical and simulational techniques applied to realistic fluid models, we elucidate how the character of these transitions depends sensitively on both the range of fluid-fluid and substrate-fluid interactions and the temperature. Our calculations uncover previously unrecognized classes of surface phase diagram which differ from that established for simple lattice models and often assumed to be universal. The differences relate both to the topology of the phase diagram and to the nature of the transitions, with a remarkable feature being a difference between drying and wetting transitions which persists even in the approach to the bulk critical point. Most experimental and simulational studies of liquids at a substrate belong to one of these previously unrecognized classes. We predict that while there appears to be nothing particularly special about water with regard to its wetting and drying behavior, superhydrophobic behavior should be more readily observable in experiments conducted at high temperatures than at room temperature.

Prediction of CO2 adsorption-induced deformation in shale nanopores

Understanding of CO2 adsorption in shale provides significant information about the potential for geological storage of CO2 in shale formations to mitigate the impact of carbon emissions on the climate. This work focuses on the adsorption behavior of CO2 in shale with various pore sizes at a wide temperature range including 31.28 °C, 40 °C, 65 °C, and 90 °C and pressures up to 15 MPa through a comprehensive model. Using a thermodynamic approach, we combine lattice density functional theory with finite element formulation to estimate CO2 adsorption behavior along with its induced strain in shale nanopores. We study the effect of geometric confinement, including pore size and pore geometry, on the excess adsorption and swelling strain of shale under different temperatures. When the model was applied to sorption of CO2 in Posidonia Shale samples, all reported experimental features of the phenomenon were reproduced. Although the developed model applied to the specific case of CO2 adsorption-induced swelling in shale, it is also applicable to any problem regarding adsorption of any fluid confined in a porous medium and its triggered swelling strain.We found that the highly confined geometry of the duct pore, which applies a large attractive surface field to adsorbed layers, leads to a faster, and a higher amount of adsorption compared with that of a slit pore. This effect is more significant in larger pore widths. The results also demonstrate a sharp rise in the adsorption isotherm and swelling strain near the bulk critical point of CO2. This phenomenon attributes to the highly compressive behavior of CO2 near its critical point, which leads to a sharp increase in bulk density and, thus, in adsorbed phase density and its resultant swelling strain. The results also denote that total volumetric strain is a function of temperature, pore width, and pore shape. The effect of pore shape and temperature is more prominent for pores with larger sizes.

Analysis of the susceptibility in a fluid system with Neumann – plus boundary conditions

The behaviour of the local and total susceptibilities of a fluid system bounded by different surfaces is studied in the framework of the Ginsburg-Landau Ising type model. The case of a plain geometry, Neumann-infinity boundary conditions under variations of the temperature and an external ordering field is considered. Exact analytic expressions for the order parameter, local and total susceptibilities in such a system are presented. They are used to analyse the phase behaviour of fluids confined in regions close to the bulk critical point of the respective infinite system.

Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption

When massless excitations are limited or modified by the presence of material bodies one observes a force acting between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg–Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) relief map of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below but close to the finite-size critical point.

Complex coacervates formed across liquid interfaces: A self-consistent field analysis

The Scheutjens–Fleer self-consistent field (SF-SCF) theory is used to study complexation between two oppositely charged polyelectrolytes across an interface formed by two solvents, here called oil and water. The focus is on the composition and the lateral stability of such interfacial coacervate. One polyelectrolyte is chosen to be oil soluble and the other one prefers water, whereas the counter and salt ions are taken to distribute ideally over all phases. There exists an electrostatic associative driving force for the formation of the coacervate phase which increases with decreasing ionic strength and may be assisted by some specific affinity between the associating units and an effective poor solvency for the coacervate. As with respect to the lateral stability an unusual wetting scenario, called pseudo-partial wetting, presents itself, which results from interactions on two different length scales. On the segmental length the screening of oil–water contacts promotes the wetting by the coacervate: a pre-wetting jump-like transition takes place off-coexistence from a microscopically thin to a mesoscopically thin film. Usually this implies complete wetting. However, the mesoscopically thin film is exposed to long-ranged attractive electrostatic interactions and therefore cannot grow to macroscopic dimensions upon approach towards coexistence. Hence the system remains partial wet. The bulk correlation length controls the thickness of the mesoscopically thin film and as a result the wetting transition occurs extremely close to the bulk critical point. We therefore expect that a thick coacervate film typically is laterally inhomogeneous: there are drops on top of a mesoscopically thin coacervate film. This conclusion qualitatively explains the experimental observation that such a coacervate film scatters visible light.

Influence of intermolecular forces at critical-point wedge filling.

We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or nonretarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated.