2nd-order Transition Research Articles

Deep learning techniques for the localization and classification of liquid crystal phase transitions

Deep Learning techniques such as supervised learning with convolutional neural networks and inception models were applied to phase transitions of liquid crystals to identify transition temperatures and the respective phases involved. In this context achiral as well as chiral systems were studied involving the isotropic liquid, the nematic phase of solely orientational order, fluid smectic phases with one-dimensional positional order and hexatic phases with local two-dimensional positional, so-called bond-orientational order. Discontinuous phase transition of 1st order as well as continuous 2nd order transitions were investigated. It is demonstrated that simpler transitions, namely Iso-N, Iso-N*, and N-SmA can accurately be identified for all unseen test movies studied. For more subtle transitions, such as SmA*-SmC*, SmC*-SmI*, and SmI*-SmF*, proof-of-principle evidence is provided, demonstrating the capability of deep learning techniques to identify even those transitions, despite some incorrectly characterized test movies. Overall, we demonstrate that with the provision of a substantial and varied dataset of textures there is no principal reason why one could not develop generalizable deep learning techniques to automate the identification of liquid crystal phase sequences of novel compounds.

An Ising Model for Supercooled Liquids and the Glass Transition

We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of (angular) momentum to proceed independently, on their own preferred time scales. The OIM also includes a third type of MC step that makes or breaks the interaction between neighboring spins, facilitating an equilibrium distribution of bond energies. MC simulations of the OIM mimic more than twenty distinctive characteristics that are commonly found above and below the glass temperature, Tg. Examples include a specific heat that has hysteresis around Tg, out-of-phase (loss) response that exhibits primary (α) and secondary (β) peaks, super-Arrhenius T dependence for the α-response time (τα), and fragilities that increase with increasing system size (N). Mean-field theory for energy fluctuations in the OIM yields a critical temperature (Tc) and a novel expression for the super-Arrhenius divergence as T→Tc: ln(τα)~1/(1−Tc/T)2. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann (VFT) law squared, we call it the “VFT2 law”. A modified Stickel plot, which linearizes the VFT2 law, shows that at high T where mean-field theory should apply, only the VFT2 law gives qualitatively consistent agreement with measurements of τα (from the literature) on five glass-forming liquids. Such agreement with the OIM suggests that several basic features govern supercooled liquids. The freezing of a liquid into a glass involves an underlying 2nd-order transition that is broadened by finite-size effects. The VFT2 law for τα comes from energy fluctuations that enhance the pathways through an entropy bottleneck, not activation over an energy barrier. Values of τα vary exponentially with inverse N, consistent with the distribution of relaxation times deduced from measurements of α response. System sizes found via the T dependence of τα from simulations and measurements are similar to sizes of independently relaxing regions (IRR) measured by nuclear magnetic resonance (NMR) for simple-molecule glass-forming liquids. The OIM elucidates the key ingredients needed to interpret the thermal and dynamic properties of amorphous materials, while providing a broad foundation for more-detailed models of liquid-glass behavior.

Disorder- driven gradual transition of the continuous symmetry- breaking phase transition

We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.

Coexisting Kondo hybridization and itinerant f -electron ferromagnetism in UGe2

Kondo hybridization in partially filled f-electron systems conveys significant amount of electronic states sharply near the Fermi energy leading to various instabilities from superconductivity to exotic electronic orders. UGe2 is a 5f heavy fermion system, where the Kondo hybridization is interrupted by the formation of two ferromagnetic phases below a 2nd order transition Tc ~ 52 K and a crossover transition Tx ~ 32 K. These two ferromagnetic phases are concomitantly related to a spin-triplet superconductivity that only emerges and persists inside the magnetically ordered phase at high pressure. The origin of the two ferromagnetic phases and how they form within a Kondo-lattice remain ambiguous. Using scanning tunneling microscopy and spectroscopy, we probe the spatial electronic states in the UGe2 as a function of temperature. We find a Kondo resonance and sharp 5f-electron states near the chemical potential that form at high temperatures above Tc in accordance with our density functional theory (DFT) + Gutzwiller calculations. As temperature is lowered below Tc, the resonance narrows and eventually splits below Tx dumping itinerant f-electron spectral weight right at the Fermi energy. Our findings suggest a Stoner mechanism forming the highly polarized ferromagnetic phase below Tx that itself sets the stage for the emergence of unconventional superconductivity at high pressure.

Absence of superconducting dome at the charge-density-wave quantum phase transition in 2H−NbSe2

Superconductivity is often found in a dome around quantum critical points, i.e. 2nd-order quantum phase transitions. Here, we show that an enhancement of superconductivity is avoided at the critical pressure of the charge-density-wave (CDW) state in NbSe$_2$. We present comprehensive high-pressure Hall effect and magnetic susceptibility measurements of the CDW and superconducting state in NbSe$_2$. Initially, the 2nd-order CDW transition is suppressed smoothly but it drops to zero abruptly at PCDW = 4.4 GPa thus indicating a change to 1st order whilstthe superconducting transition temperature Tc rises continuously up to PCDW but is constant above. The putative 1st-order nature of the CDW transition is suggested as the cause for the absence of a superconducting dome at PCDW. Indeed, we show that the suppression of the superconducting state at low pressures is due to the loss of density of states inside the CDW phase whilst the initial suppression of the CDW state is accounted for by the stiffening of the underlying bare phonon mode.

Capping agents as a novel approach to control VO2 nanoparticles morphology in hydrothermal process: Mechanism of morphology control and influence on functional properties

A novel approach to regulate nanoparticles morphology using capping agents (etidronic, succinic, tartaric and salicylic acids) in hydrothermal synthesis is presented. UV–Vis and FTIR spectra showed that influence of the capping agents is based on the interaction with particles surface during the solid phase formation. For na-VO2 nanorods a 1st order phase transition at 275 K was demonstrated using vibration sample magnetometry. Differential scanning calorimetry showed that this transition is accompanied by 2nd order transition at 320 K. Decrease in rods thickness and length for sal-VO2 and suc-VO2 made the transition less expressed and its temperature lowered from 275 to 150 K. Addition of tartaric and etidronic acids led to change of particles shape from rods to spheres and eliminated all the transitional changes in magnetic properties. Charge-discharge tests revealed that initial discharge capacity of nanorods was 100 mA h g−1, which is three times higher than that of spheres.

Development of thermodynamic database for high Mn–high Al steels: Phase equilibria in the Fe–Mn–Al–C system by experiment and thermodynamic modeling

Fe–Mn–Al–C system is a core system of high Mn–high Al steels for applications in automotive, cryogenic, electrical steels, etc. In order to provide an efficient tool for alloy/process design, a thermodynamic database of the quaternary system was developed in the present study by experimental phase diagram study coupled with CALPHAD type thermodynamic modeling. All stable phases relevant to steel matrix and precipitates including κ-carbide and bcc_B2 (α′) were considered in the modeling. High temperature equilibrated samples followed by an electron microscopy analysis showed that steel matrix of the austenite (γ) was observed often to be in equilibrium with the κ-carbide. Homogeneous region of the γ enlarged by increasing Mn content up to 20mass%, then shrinked by further increasing the Mn content up to 40mass%. The phase diagram information experimentally determined in the present study and those reported in the literature were utilized in order to model Gibbs energies of the relevant phases. The Compound Energy Formalism (CEF) was used for each solid solution with proper consideration of its crystal structure. In particular, the κ-carbide was modeled by a formula (Fe,Mn)3(Fe,Mn,Al)1(Va,C)1 and α′ was modeled by a formula (Fe,Mn,Al)0.5(Fe,Mn,Al)0.5(Va,C)3 in order to take into account A2/B2 (α/α′) 2nd order transition, as being important intermetallic precipitates. The Modified Quasichemcial Model in the pair approximation was employed for the liquid phase in order to take into account strong chemical interactions among components. The obtained Gibbs energy equations form a complete thermodynamic database for the Fe–Mn–Al–C system. It can be used to predict alloy phase equilibria of the system, and also can be a part of larger multicomponent steel database.

Bounds on universal quantum computation with perturbed two-dimensional cluster states

Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of perturbed 2d cluster states, we find strong evidence of a very well defined cluster phase, separated from a polarized phase by a line of 1st and 2nd order transitions compatible with the 3d Ising universality class and a tricritical end point. The phase boundary sets an upper bound for the amount of perturbation in the system so that its ground state is still useful for measurement-based quantum computation purposes. Moreover, we also compute the local fidelity with the unperturbed 2d cluster state. Besides a classical approximation, we determine the phase diagram by combining series expansions and variational infinite Projected entangled-Pair States (iPEPS) methods. Our work constitutes the first analysis of the non-trivial effect of few-body perturbations in the 2d cluster state, which is of relevance for experimental proposals.

Phase transitions in the two-dimensional superantiferromagnetic Ising model with next-nearest-neighbor interactions

We use Monte Carlo and transfer matrix methods in combination with extrapolation schemes to determine the phase diagram of the two-dimensional superantiferromagnetic (SAF) Ising model with next-nearest-neighbor (NNN) interactions in a magnetic field. The interactions between nearest-neighbor (NN) spins are ferromagnetic along x, and antiferromagnetic along Y. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of second-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with reentrant behavior. The NNN couplings produce either an expansion or a contraction of the SAF phase. Expansion occurs when the interactions are antiferromagnetic, and contraction when they are ferromagnetic. There is a critical ratio R(c)=1/2 between NNN and NN couplings, beyond which the SAF phase no longer exists.

On finite-temperature holographic QCD in the Veneziano limit

Abstract Holographic models in the T = 0 universality class of QCD in the limit of large number N c of colors and N f massless fermion flavors, but constant ratio x f = N f /N c, are analyzed at finite temperature. The models contain a 5-dimensional metric and two scalars, a dilaton sourcing TrF 2 and a tachyon dual to $ \overline{q}q $ . The phase structure on the T, x f plane is computed and various 1st order, 2nd order transitions and crossovers with their chiral symmetry properties are identified. For each x f , the temperature dependence of p/T 4 and the condensate $ \left\langle {\overline{q}q} \right\rangle $ is computed. In the simplest case, we find that for x f up to the critical x c ~ 4 there is a 1st order transition on which chiral symmetry is broken and the energy density jumps. In the conformal window x c < x f < 11/2, there is only a continuous crossover between two conformal phases. When approaching x c from below, x f → x c, temperature scales approach zero as specified by Miransky scaling.

Quantum Phases of Excitons and Their Detections in Electron-Hole Semiconductor Bilayer Systems

There have been extensive experimental search for possible exciton superfluid in semiconductor electron-hole bilayer (EHBL) systems below liquid Helium temperature. Here we construct a quantum Ginsburg-Landau theory to study the quantum phases and transitions in EHBL. We propose that in the dilute limit as distance is increased, there is a first order transition from the excitonic superfluid (ESF) to the excitonic supersolid (ESS) driven by the collapsing of a roton minimum, then a 2nd order transition from the ESS to excitonic normal solid. We show the latter transition is in the same universality class of superfluid to Mott transition in a rigid lattice. We then study novel elementary low energy excitations inside the ESS. We find that there are two “supersolidon” longitudinal modes (one upper branch and one lower branch) inside the ESS, while the transverse mode in the ESS stays the same as that inside a exciton normal solid (ENS). We also work out various experimental signatures of these novel elementary excitations by evaluating the Debye-Waller factor, density-density correlation, specific heat and vortex-vertex interactions. For the meta-stable supersolid generated by photon pumping, we show that several unique features of the photoluminescent can be used to detect the metastable ESS state generated by photon pumping without any ambiguity.

The correlation contracted Schrödinger equation: An accurate solution of the G‐particle‐hole hypervirial

AbstractThe equation obtained by mapping the matrix representation of the Schrödinger equation with the 2nd‐order correlation transition matrix elements into the 2‐body space is the so called correlation contracted Schrödinger equation (CCSE) (Alcoba, Phys Rev A 2002, 65, 032519). As shown by Alcoba (Phys Rev A 2002, 65, 032519) the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the correlation operator (GHV), which can be identified with the anti‐Hermitian part of the CCSE. A comparative analysis of the GHV and the anti‐Hermitian part of the contracted Schrödinger equation (ACSE) indicates that the former is a stronger stationarity condition than the latter. By applying a Heisenberg‐like unitary transformation to the G‐particle‐hole operator (Valdemoro et al., Phys Rev A 2000, 61, 032507), a good approximation of the expectation value of this operator as well as of the GHV is obtained. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li2 and BeH2 molecules. The correlation energies obtained are within 98.80–100.09% of the full‐configuration interaction ones. The convergence of these calculations was faster when using the GHV than with the ACSE. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Transport properties near the magneto/structural transition of Tb5Si2Ge2

Abstract We report high resolution measurements of the electrical resistivity (ρ, dρ/dT) and thermopower (S, dS/dT) measurements near the magnetic and structural transition of the layered Tb5Si2Ge2 compound, which are fairly close but not fully coupled. The analysis of the transport properties confirms a split magneto/structural transition, with TS ∼ 97 K and TS ∼ 107 K for the structural transition (on cooling and heating respectively; 1st-order transition). The magnetic transition occurs only at TC ∼ 112 K and without hysteresis (2nd-order transition). The magnetic critical behavior of resistivity is analyzed, obtaining an almost classical mean field exponent (α ∼ 0.59) for T > TC. For the structural phase, and below TS, we obtain a rather different exponent (α ∼ 1.06).

Phase structure of the massive chiral Gross-Neveu model from the Hartree-Fock approach

The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu--Jona-Lasinio model in $1+1$ dimensions) is constructed. In the large $N$ limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature, and compared with the one of the discrete chiral Gross-Neveu model. As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.

Tricritical behavior of the massive chiral Gross-Neveu model

The phase diagram of the massive chiral Gross-Neveu model (the $1+1$-dimensional Nambu-Jona-Lasinio model at large $N$) is investigated in the vicinity of the tricritical point. Using the derivative expansion, the grand canonical potential is cast into the form of a Ginzburg-Landau effective action. Minimization of this action by variational and numerical methods reveals both 1st and 2nd order phase transitions to a chiral crystal phase, separated by a tricritical line. These findings are contrasted to the massive Gross-Neveu model with discrete chiral symmetry where only 2nd order transitions have been observed.

Evaluation of the stochastic weather generators LARS-WG and AAFC-WG for climate change impact studies

There is a need to know how well stochastic weather generators can produce daily climate scenarios for climate change impact studies. In this study, 2 stochastic weather generators (LARS-WG and AAFC-WG) were assessed, based on an experiment with historical daily climate data. The experiment was conducted for 3 stations in Canada, using 1911-1940 as the baseline climate period and 1971-2000 as the changed climate period. Weather generators were calibrated with the baseline data. Daily climate scenarios were then generated for 1971-2000, using parameters that were adjusted to reflect climate change. Different schemes for modifying weather generator parameters were assessed in relation to their capability to reproduce statistical properties of daily climate data for a changed climate. Using changes in the statistics of daily climate data between the baseline climate and the changed climate period, it became feasible to modify parameters for the weather generators that use empirical distributions. For reproducing changes in frequency of wet and dry spells, modification schemes with a full adjustment (all 2nd order transition probabilities being modified separately) for the 2nd order Markov chain appeared more effective than the modifi- cation to mean length of wet and dry spells. Separate adjustments for maximum (Tx) and minimum (Tn) temperature, rather than modification on the basis of changes in daily mean temperature, might also be necessary. The probability distribution of daily precipitation amount (P) in a changed climate seemed more difficult to simulate well, although the means and variances were produced better. In general, daily climate scenarios developed by weather generators can be reasonably reliable for agri- cultural impact studies, provided the changes in the statistics of daily weather variables from daily GCM output are reliable. Otherwise, downscaling may be required to obtain reliable changes in the statistics of local daily weather variables.

DENSITY-OF-STATES MONTE CARLO METHOD FOR SIMULATION OF TWO-DIMENSIONAL RANDOM BOND POTTS MODEL

Softening of the phase transition and critical phenomena for the 2D random-bond Potts ferromagnet is investigated by using the density-of-states Monte Carlo method to calculate the thermodynamic properties with a variety of the quenched bond-randomness characterized by a disorder amplitude r=Ks/Kw. The numerical results show that the crossover from the 1st- to 2nd-order transition was induced at finite lattices for the self-dual bimodal distribution.

Heavy-mass fermi liquid near a ferromagnetic instability in layered ruthenates.

Low temperature magnetic, thermal, and transport measurements in Ca2-xSrxRuO4 clarify the appearance of a cluster glass phase, after the evolution of a nearly ferromagnetic heavy-mass Fermi liquid from the spin-triplet superconductor Sr2RuO4. As the Mott transition is approached across a 2nd-order structural transition, both the magnetization and specific heat decrease considerably while the transport scattering rate diverges. A metamagnetic transition to a highly spin polarized state, with a local moment S=1/2, is observed. We argue that an orbital rearrangement with Ca substitution changes itinerant ferromagnetism to antiferromagnetism of localized moments.

Sign‐singularity analysis of current disruption

The sign‐singular measure analysis is a new tool to investigate the scaling features of signals which oscillate in sign on an arbitrarily fine scale. In this work, we apply this new tool to the magnetic fluctuations observed before, during, and after tail current disruption (CD). The analysis shows that sign‐singularity is a genuine feature of the magnetic fluctuations in the near‐tail region, and that the character of the sign‐singularity changes during CD. Different values of the sign‐singularity scaling index, named the cancellation exponent κ, are obtained for periods before, during and after the CD. This change of the cancellation exponent is indicative of a reorganization phenomenon, occurring during CD. The results are discussed in connection with magnetospheric substorm onset as well as in the framework of self‐organized criticality and 2nd phase order transition.

Transitiometric Analysis of Pressure Effects on Various Phase Transitions

A scanning transitiometer has been used in investigations of 1st and 2nd order phase transformations in polymers. It was demonstrated taking as an example fusion of polyethylene at 200 MPa with a temperature scan as inducing variable that by recording simultaneously the rate of heat exchange and the rate of volume variations it is possible to determine in a single experiment the pressure derivative of temperature of this 1st order phase transition. For phase transformations similar to the 2nd order transitions the transitiometric analysis permits simultaneous measurements of pairs of thermodynamic derivatives which permit determination of pressure effects according to the Ehrenfest equations. For the glass transition in polystyrene at high pressures the pressure effect was similar independently of the pair of thermodynamic derivatives used (heat capacity and thermal expansivity or compressibility and thermal expansibility).