Vicinity Of Phase Transition Research Articles

Simulating first-order phase transition with hierarchical autoregressive networks.

We apply the hierarchical autoregressive neural network sampling algorithm to the two-dimensional Q-state Potts model and perform simulations around the phase transition at Q=12. We quantify the performance of the approach in the vicinity of the first-order phase transition and compare it with that of the Wolff cluster algorithm. We find a significant improvement as far as the statistical uncertainty is concerned at a similar numerical effort. In order to efficiently train large neural networks we introduce the technique of pretraining. It allows us to train some neural networks using smaller system sizes and then employ them as starting configurations for larger system sizes. This is possible due to the recursive construction of our hierarchical approach. Our results serve as a demonstration of the performance of the hierarchical approach for systems exhibiting bimodal distributions. Additionally, we provide estimates of the free energy and entropy in the vicinity of the phase transition with statistical uncertainties of the order of 10^{-7} for the former and 10^{-3} for the latter based on a statistics of 10^{6} configurations.

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible universal characteristics in the non-equilibrium evolution of systems in quantum critical phases. In this context, universality is generically attributed to the insensitivity of observables to the microscopic system parameters and initial conditions. Here, we present such a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian – a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quantum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-of-the-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov–Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret–Markov approximations, which contrary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian.

Precision study of the continuum SU(3) Yang-Mills theory: How to use parallel tempering to improve on supercritical slowing down for first order phase transitions

We perform large scale simulations to characterize the transition in quenched QCD. It is shown by a rigorous finite size scaling that the transition is of first order. After this qualitative feature quantitative results are obtained with unprecedented precision: we calculate the transition temperature $w_0T_c$=0.25384(23), -- which is the first per-mill accurate result in QCD thermodynamics -- and the latent heat $\Delta E/T_c^4$=1.025(21)(27) in both cases carrying out controlled continuum and infinite volume extrapolations. As it is well known the cost of lattice simulations explodes in the vicinity of phase transitions, a phenomenon called critical slowing down for second order phase transitions and supercritical slowing down for first order phase transitions. We show that a generalization of the parallel tempering algorithm of Marinari and Parisi [Europhys. Lett. 19, 451 (1992)] originally for spin systems can efficiently overcome these difficulties even if the transition is of first order, like in the case of QCD without quarks, or with very heavy quarks. We also report on our investigations on the autocorrelation times and other details.

Local phase transition at crack edges of Mo1−xWxTe2 polymorphs

The phase engineering of two-dimensional (2D) materials has attracted considerable attention in recent years, but nanometer-scale samples and experimental techniques have limited the rigorous study of the local phase engineering of 2D atomic crystals. Here, we report on a nanometer-scale probe of phase evolution in the Mo1−xWxTe2 alloys, which exhibit a structural transition between the semiconducting 2H phase and the metallic 1T′ phase. We found that many crack edges are created by the accumulated tungsten atoms, resulting in poor crystallinity in the 2H-Mo1−xWxTe2 flakes at the vicinity of phase transition with a tungsten content, x = 0.08. With mild laser irradiation of the 2H-Mo1−xWxTe2 flakes, the 2H phase region near a crack edge was easily converted to the 1T′ phase, while other areas apart from the crack edge region retained their 2H phase under the same laser treatment. Our study clarifies the role of locally accumulated atoms and crystallinity for the phase engineering of 2D materials, which opens the way to various applications based on heterophase structures, ranging from energy conversion and storage to optoelectronic devices.

Dielectric, Pyroelectric and Ferroelectric Properties of Sn2P2(Se x S1- x )6 Single Crystals

Sn2P2(Se x S1- x )6 (x = 0.1, 0.2 and 0.3) crystals were grown by the vapor transport technique and their dielectric, pyroelectric and ferroelectric properties in the vicinity of phase transition were evaluated. The dielectric properties of the investigated crystals show clear anomalies associated with the ferroelectric-paraelectric phase transitions in all the compositions. The spontaneous polarization behavior of Sn2P2(Se x S1- x )6 crystals in the vicinity of the ferroelectric-paraelectric phase transition is discussed. The knowledge about the ferroelectric responses of Sn2P2(Se x S1- x )6 crystals in a broad temperature range is essential for applications in the energy storage technology. The aim of this work was to investigate the dielectric, pyroelectric and ferroelectric properties of Sn2P2(Se x S1- x )6 with different selenium content and compare to the parent compounds Sn2P2S6 and Sn2P2Se6.

Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set—the intrinsic dimension (Id)—behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based Id estimators to compute the Id of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the Id uniquely characterizes the transition regime. The finite-size analysis of the Id allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent ν in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.8 MoreReceived 3 July 2020Revised 9 November 2020Accepted 15 December 2020DOI:https://doi.org/10.1103/PhysRevX.11.011040Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasClassical statistical mechanicsPhase transitionsTechniquesData miningMachine learningCondensed Matter, Materials & Applied PhysicsStatistical Physics

Elastic and anelastic properties of vinylidene fluoride-trifluoroethylene (VDF-Tr) copolymers in the vicinity of phase transition

Temperature dependences of internal friction Q−1 and elastic modulus E of the VDF60Tr40 copolymer were studied in the temperature range of 20–100 °C at a frequencies f ≈ 3–17 Hz. A distinct softening of the modulus E was found near the Curie temperature. In the vicinity of 60 °C, a wide maximum of Q−1 is revealed, which is a superposition of two Q−1 peaks. The “low-temperature” peak of internal friction is due to the process of α-relaxation in the non-crystalline polymer fraction. “High-temperature” one is associated with a first-order ferroelectric phase transition in the crystalline fraction.

Dielectric Spectra of TGS + Сr Crystals in the Vicinity of Phase Transition

Dependencies of the complex permittivity of chromium-doped ferroelectric triglycine sulfate crystals (TGS + Cr) have been measured using dielectric spectroscopy method in a frequency range of 1–107 Hz and a temperature range of 23–60°C upon heating and cooling. The dielectric spectra are analyzed by considering the temperature‒frequency dependences of the real (e') and imaginary (e") parts of permittivity in the immediate vicinity of the phase transition using the dynamic conductance model and taking into account resonance processes. Good agreement between calculated and experimental data is obtained for the dielectric response of TGS + Cr crystal near the Curie temperature.

Spinon confinement and deconfinement in spin-1 chains

Motivated by the rich phase diagrams recently unveiled in frustrated spin-1 chains with competing next-nearest neighbour and four-spin interactions, we investigate the nature of the elementary excitations of spin-1 chains in the vicinity of phase transitions using the matrix-product state (MPS) representation of elementary excitations. First, we show that both spinons and magnons naturally arise in SU(2) invariant spin chains when describing ground states and elementary excitations using MPS. Then we investigate the nature of the elementary excitations across the first-oder transition between the Haldane phase and the topologically trivial next-nearest neighbor Haldane phase. We show explicitly that spinons deconfine at the transition, and we calculate the dispersion of these deconfined spinons with MPS. We also show that, immediately away from the transition line, spinons confine, forming dispersive spinon/anti-spinon bound states on both sides of the transition. Finally, we show that deconfined spinons also appear at the transition between the Haldane phase and the spontaneously dimerized phase when this transition is first order.

Generalized coherent-squeezed-state expansion for the super-radiant phase transition

We develop a systematic variational coherent-squeezed-state expansion for the ground state of the quantum Rabi model, which includes an additional squeezing effect with comparisons to previous coherent-state approach. For finite large ratio between the atomic and field frequency, the essential feature of the ground-state wave function in the super-radiant phase appears, which has a structure of two delocalized wake packets. The single-peaked wave function with one coherent-squeezed state works well even around the critical regime, exhibiting the advantage over the coherent-state method. As the coupling increases to form strong correlations physics in the vicinity of phase transition, we develop an improved wave function with a structure of two Gaussian wave packets, which is a linear superposition of two coherent-squeezed state. The ground-state energy and the average photon number agree well with numerical ones even in the strong-correlated regimes, exhibiting a substantial improvement over the coherent-state expansion. The advantage of the coherent-squeezed-state expansion lies in the inclusion of the second coherent-squeezed state and the additional squeezed deformation of the wave function, providing a useful tool for multi-modes spin-boson coupling systems of greater complexity.

Unique Freezing Dynamics of Flexible Guest Cations in the First Molecular Postperovskite Ferroelectric: (C 5 H 13 NBr)[Mn(N(CN) 2 ) 3

Ferroelectricity is usually found in cubic and hexagonal perovskites consisting of corner- and faced-shared BX6 octahedra, respectively. In contrast, another important branch of perovskites, postpe...

Grand Unified Theories of the Brain Need Better Understanding of Behavior: The Two-Tiered Emergence of Function

Over the last few decades, neuroscience and various associated disciples have expanded enormously in terms of output, tools, methods, concepts, and large-scale projects. In spite of these developments, the principles underlying brain function and behavior are yet only partially understood. We claim that brain functioning requires the elucidation of the rules associated with all possible task realizations, rather than targeting the activity underlying a specific realization. A first step in that direction was taken by approaches focusing on dynamical structures underlying task performances, as exemplified by coordination dynamics. Its theoretical foundation owes much to Haken’s synergetics, which provides a formalism through which the degrees of freedom associated with high-dimensional systems may be effectively reduced to one or a few functional variables in the vicinity of phase transitions. The recent theoretical development of structured flows on manifolds (SFM) allows the employment to a potentially broader range of applications. Here we expand the SFM framework and propose that the emergent two-tiered fast–slow dynamics may be a basic mathematical organization underlying the architecture of brain and behavior dynamics. Finally, along a few examples, we illustrate how this framework allows for the incorporation of notions cardinal to ecological psychology.

Dielectric, pyroelectric and ferroelectric properties of lead-doped Sn2P2S6 crystals

ABSTRACTThe dielectric, pyroelectric and ferroelectric properties of (PbySn1−y)2P2S6 (y = 0.1, 0.2 and 0.3) single crystals were analysed in the vicinity of phase transition. The measurements were done covering a wide range of frequency (20 Hz to 1 MHz) and temperature (30350 K) range. Structural phase transition temperature decreases with increased lead concentration and evokes the broadening of the dielectric anomaly. The features of this phase transition are discussed and related to stereoactivity of Sn2+ ions and fluctuations of the concentration of Pb2+ ions. Pyroelectric measurements were performed from 190 K to 325 K during the heating cycle. These investigations showed that an increase of lead concentration does not affect the maximum value of pyroelectric coefficient, and the maximum values of pyroelectric coefficients γmax which (in the vicinity of the phase transition temperature) are nearly equal to 250 nC cm−2 K−1 for all the compositions. The temperature evolution of polarization hysteresis loops proved crystals being ferroelectrics.

Ultrafast polarization switching of (BaSr)TiO3 thin film by a single-period terahertz pulse in a vicinity of phase transition

We report here an experimental and theoretical study on ultrafast switching of dielectric polarization in (Ba0.8Sr0.2)TiO3 thin films by a strong electric field of a nearly single-cycle THz pulse at different temperatures. Optical second harmonic generation (SHG) is used as a probe of the polarization in the terahertz pump-optical probe experiment. We describe an approach to interpretation of SHG response from the ferroelectric polydomain film excited by a short electric field pulse. We show that dielectric polarization induced by the THz field decreases while approaching the Curie temperature. Simulations with the help of the Duffing equation reproduce the experimental observations.

Electrosorption of a modified electrode in the vicinity of phase transition: A Monte Carlo study

Fil: Gavilan Arriazu, Edgardo Maximiliano. Universidad Nacional de Santiago del Estero. Instituto de Bionanotecnologia del Noa. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Tucuman. Instituto de Bionanotecnologia del Noa; Argentina

Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding.

The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.

Fractional Stability of Trunk Acceleration Dynamics of Daily-Life Walking: Toward a Unified Concept of Gait Stability.

Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transitions. In this case the temporal change in distance, d(t), between neighboring trajectories in state space is assumed to be an exponential function of time. However, results from walking models and empirical studies show that the assumptions of exponential stability break down in the vicinity of phase transitions that are present in each step cycle. Here we apply a general non-exponential construct of gait stability, called fractional stability, which can define dynamic stability in the presence of phase transitions. Fractional stability employs the fractional indices, α and β, of differential operator which allow modeling of singularities in d(t) that cannot be captured by exponential stability. The fractional stability provided an improved fit of d(t) compared to exponential stability when applied to trunk accelerations during daily-life walking in community-dwelling older adults. Moreover, using multivariate empirical mode decomposition surrogates, we found that the singularities in d(t), which were well modeled by fractional stability, are created by phase-dependent modulation of gait. The new construct of fractional stability may represent a physiologically more valid concept of stability in vicinity of phase transitions and may thus pave the way for a more unified concept of gait stability.

Low-frequency noise characteristics of lamellar ferrielectric crystal CuInP2S6 at the phase transition

The detailed investigations of low-frequency noise characteristics of a ferrielectric CuInP2S6 crystal are presented at the vicinity of phase transition. The white noise spectra are observed at room temperature. Voltage noise spectra are characterized by 1/f noise above the phase transition temperature. Lorentzian-type spectra were applied to investigate the normalized voltage fluctuation density, in order to obtain a deeper insight into the phenomenon of 1/f noise in the CuInP2S6 crystal. The analysis of experimental data revealed that the source of the 1/f noise in the CuInP2S6 crystal is the carrier number fluctuation due to the recombination between defect levels. The obtained results indicate noise spectroscopy as being a reliable, sensitive, and non-destructive tool complementary to the other measurement techniques for the characterization of ferroelectric materials.

Physical properties of Polyakov loop geometrical clusters in SU(2) gluodynamics

We apply the liquid droplet model to describe the clustering phenomenon in SU(2) gluodynamics, especially, in the vicinity of the deconfinement phase transition. In particular, we analyze the size distributions of clusters formed by the Polyakov loops of the same sign. Within such an approach this phase transition can be considered as the transition between two types of liquids where one of the liquids (the largest droplet of a certain Polyakov loop sign) experiences a condensation, while the other one (the next to largest droplet of opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two accompanying gases, and their size distributions are described by the liquid droplet parameterization. By fitting the lattice data we have extracted the value of Fisher exponent τ=1.806±0.008. Also we found that the temperature dependences of the surface tension of both gaseous clusters are entirely different below and above the phase transition and, hence, they can serve as an order parameter. The critical exponents of the surface tension coefficient in the vicinity of the phase transition are found. Our analysis shows that the temperature dependence of the surface tension coefficient above the critical temperature has a T2 behavior in one gas of clusters and T4 in the other one.

Evolution of the domain structure of triglycine sulphate single crystal in the vicinity of phase transition

ABSTRACTThe temporal behavior of the domain structure of triglycine sulphate single crystal (TGS) was studied by means of atomic force microscopy near the phase transition temperature: 321 K ≤ T <TC = 322 K. It is shown that the total number of domains and their total linear dimensions along two selected directions decrease exponentially in time. The average linear dimensions of domains along nearly [001] and [100] directions obey to the law: <w> ∼ tϕ. The exponent ϕ varies from 0,45 to 0,93. These values indicate to the non-conservative nature of macroscopic order parameter characterizing the domain structure of TGS in the temperature interval under study. A character of time dependence of the average velocity of lateral movement (nearly along [001]) of the domain walls changes qualitatively when removing from the phase transition temperature.