Fluctuations Of Order Parameter Research Articles

Thermodynamic Quantities of Morse Fluids in the Supercritical Region

The critical point parameters for liquid alkali metals (sodium and potassium) are calculated accounting for the non-Gaussian order parameter fluctuations and the Morse interaction potential. The behavior of the isothermal compressibility, density fluctuations, and thermal expansion for sodium is studied in the supercritical temperature region. A significant increase in the isothermal compressibility and the density fluctuations near the critical point indicates a substantial density sensitivity to tiny pressure fluctuations. The thermal expansion coefficient for various fixed pressure values shows a typical gas decrease with increasing supercritical temperature. The Widom line separating the gaseous and liquid structures of the fluid at temperatures above the critical one is represented. Note that our calculations are valid in a small neighborhood of the critical point, which is problematic for theoretical and experimental studies.

Mixing Properties of Cu-Mg Liquid Alloy Using Exponential Model

The Redlich-Kister (R-K) polynomial has been generally used to model the mixing properties of binary and higher order alloys. The interaction energy parameters of the R-K polynomial are assumed to be either linear or exponentially temperature-dependent. When these parameters are assumed to be linear temperature-dependent, the computed thermodynamic functions sometimes show unusual trends. But when they are assumed to be exponential temperature-dependent, such trends do not appear in the theoretical calculations. Therefore, the mixing properties of Cu-Mg liquid alloy have been studied using the exponential temperature-dependent parameters of the above-mentioned model. These parameters for excess Gibb’s free energy of mixing have been optimised using the experimental values of enthalpy of mixing and excess entropy of mixing. The study of thermodynamic properties involves the measurement of excess Gibb’s free energy of mixing, enthalpy of mixing and activities of monomers at different temperatures. Likewise, the assessment of surface property includes surface tension and surface concentration. Similarly, the structural properties have been studied by computing concentration fluctuation in long wave-length limit and short-range order parameter at different temperatures. The investigation revealed that the exponential model can explain mixing behavior of Cu-Mg liquid alloy and the system is found to have strong compound forming tendency at its melting temperature. This mixing tendency has been observed to decrease with the increase in temperature above its melting temperature.

Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model

We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider time-reversal-symmetric systems with uniform (i.e., at both low-momentum and low-frequency) pairing fluctuations in a unit cell, and derive the corresponding time-dependent Ginzburg-Landau (TDGL) equation. In addition to the conventional intraband contribution that depends on the derivatives of the Bloch bands, we show that the kinetic coefficients of the TDGL equation have a geometric contribution that is controlled by both the quantum-metric tensor of the underlying Bloch states and their band-resolved quantum-metric tensors. Furthermore we show that thermodynamic properties such as London penetration depth, GL coherence length, GL parameter and upper critical magnetic field have an explicit dependence on quantum geometry.

Ultrafast melting of charge-density wave fluctuations at room temperature in 1T-TiSe2 monitored under non-equilibrium conditions

We investigate the ultrafast lattice dynamics in 1T-TiSe2 using femtosecond reflection pump–probe and pump–pump–probe techniques at room temperature. The time-domain signals and Fourier-transformed spectra show the A1g phonon mode at 5.9 THz. Moreover, we observe an additional mode at ≈ 3 THz, corresponding to the charge-density wave (CDW) amplitude mode (AM), which is generally visible below Tc≈200 K. We argue that the emergence of the CDW amplitude mode at room temperature can be a consequence of fluctuations of order parameters based on the additional experiment using the pump–pump–probe technique, which exhibited suppression of the AM signal within the ultrafast timescale of ∼0.5 ps.

How Infrared Singularities Affect Nambu–Goldstone Bosons at Finite Temperatures

Ordered phases realized through broken continuous symmetries embrace long-range order-parameter fluctuations as manifest in the power-law decays of both the transverse and longitudinal correlations, which are similar to those at the second-order transition point. We calculate the transverse one-loop correction to the dispersion relation of nonrelativistic Nambu-Goldstone (NG) bosons at finite temperatures, assuming that they have well-defined dispersion relations with some integer exponents. It is found that the transverse correlations make the lifetime of the NG bosons vanish right on the assumed dispersion curve below three dimensions at finite temperatures. Combined with the vanishing of the longitudinal "mass", the result indicates that the correlations generally bring both an intrinsic lifetime to the excitations and a qualitative change in the dispersion relation at long wavelengths below three dimensions at finite temperatures, unless it is protected by some conservation law. A more detailed calculation performed specifically on a single-component Bose-Einstein condensate reveals that the gapless Bogoliubov mode predicted by the perturbative treatment is modified substantially after incorporating the correlations to have (i) an intrinsic lifetime and (ii) a peak shift at long wavelengths from the linear dispersion relation. Thus, the NG bosons may be fluctuating intrinsically into and out of the ordered "vacuum" to maintain the order temporally.

Quantum quenches of an SO(5) pseudospin reveal Higgs bosons

A controlled dynamical probe measurement of complex order parameter fluctuations of a system may reveal its massive collective excitations. Here, we design dynamical quench protocols to excite independently all ten midgap Higgs bosons in the isotropic Balian-Werthamer state of a spinful $p$-wave superfluid or superconductor. The analysis is based on microscopic equations of motion of an SO(5) pseudospin, an extension of the usual Bloch equation to a five-dimensional space. Key to these protocols is the realization of quenches that break the rotational symmetry of the kinetic energy and exploit the irreducible representation of the angular momentum $J=2$. For perturbative quenches, we find (nondecaying) periodic oscillations in time of these Higgs modes. We present experimental protocols for superconductors (superfluids), with the intention of unveiling the nature of their order parameters.

Absence of Ginzburg-Landau mechanism for vestigial order in the normal phase above a two-component superconductor

A two-component superconductor may hypothetically support a vestigial order phase above its superconducting transition temperature, with rotational or time-reversal symmetry spontaneously broken while remaining nonsuperconducting. This has been suggested as an explanation for the observed normal state nematicity of the nematic superconductor ${M}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. We examine the condition for this vestigial order to occur within Ginzburg-Landau theory with order parameter fluctuations, on both the nematic and chiral sides of the theory. Contrary to prior theoretical results, we rule out a large portion of parameter space for possible vestigial order. We argue that very extreme anisotropy is one prerequisite for the formation of a stable vestigial phase via this mechanism, which is likely not met in real materials.

Dissipative Quantum Criticality as a Source of Strange Metal Behavior

The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.

Stability of the Néel quantum critical point in the presence of Dirac fermions

We investigate the stability of the N\'eel quantum critical point of two-dimensional quantum antiferromagnets, described by a nonlinear $\ensuremath{\sigma}$ model, in the presence of a Kondo coupling to ${N}_{f}$ flavors of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using the momentum-shell renormalization group (RG), we demonstrate that the Landau damping is weakly irrelevant at the N\'eel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the N\'eel quantum critical point quasistable for ${N}_{f}\ensuremath{\ge}4$ and thermodynamically stable for ${N}_{f}<4$. In the latter case, we identify a multicritical point which describes the transition between the N\'eel critical and Kondo runaway regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multicritical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.

Fractal Fluctuations at Mixed-Order Transitions in Interdependent Networks.

We study the critical features of the order parameter's fluctuations near the threshold of mixed-order phase transitions in randomly interdependent spatial networks. Remarkably, we find that although the structure of the order parameter is not scale invariant, its fluctuations are fractal up to a well-defined correlation length ξ^{'} that diverges when approaching the mixed-order transition threshold. We characterize the self-similar nature of these critical fluctuations through their effective fractal dimension d_{f}^{'}=3d/4, and correlation length exponent ν^{'}=2/d, where d is the dimension of the system. By analyzing percolation and magnetization, we demonstrate that d_{f}^{'} and ν^{'} are the same for both, i.e., independent of the symmetry of the process for any d of the underlying networks.

Effective Fractal Dimension at 2d-3d Crossover

This article is aimed at reviewing and studying the effects of the 2d-3d crossover on the effective fractal and spatial dimensions, as well as on the critical exponents of the physical properties of bulk and bounded systems at criticality. Here we consider the following problems: (1) the two types of dimensional crossovers and the concept of the universality classes; (2) a smooth 2d-3d crossover and the calculation of the effective fractal and spatial dimensions, as well as the effective critical indices; (3) the fractal dimension, its connection with the random mean square order-parameter fluctuations and a new phase formation; (4) the fractal nuclei of a new phase and the medical consequences of carcinogenesis and nucleation isomorphism.

Turbulent route to two-dimensional soft crystals.

We investigate the effect of a two-dimensional, incompressible, turbulent flow on soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag and short-range interparticle interactions. We quantify this phase through the bond order parameter and local density fluctuations and find a sharp transition between the crystalline and noncrystalline phases as a function of the Stokes number. Furthermore, the nature of preferential concentration, characterized by the correlation dimension, is significantly different from that of particle-laden flows in the absence of repulsive potentials.

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice -- such as $(p_{x},\,p_{y})$-wave and $(d_{x^{2}-y^{2}},\,d_{xy})$-wave. Such a system has two possible superconducting states: the chiral state (e.g. $p+ip$ or $d+id$), which breaks time-reversal symmetry, and the nematic state (e.g. $p+p$ or $d+d$), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A non-analytic cubic term arises, as in the case of a conventional $s$-wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. We analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

Order Parameter and Entropy of Seismicity in Natural Time before Major Earthquakes: Recent Results

A lot of work in geosciences has been completed during the last decade on the analysis in the new concept of time, termed natural time, introduced in 2001. The main advances are presented, including, among others, the following: First, the direct experimental verification of the interconnection between a Seismic Electric Signals (SES) activity and seismicity, i.e., the order parameter fluctuations of seismicity exhibit a clearly detectable minimum when an SES activity starts. These two phenomena are also linked closely in space. Second, the identification of the epicentral area and the occurrence time of an impending major earthquake (EQ) by means of the order parameter of seismicity and the entropy change of seismicity under time reversal as well as the extrema of their fluctuations. An indicative example is the M9 Tohoku EQ in Japan on 11 March 2011. Third, to answer the crucial question—when a magnitude 7 class EQ occurs—whether it is a foreshock or a mainshock. This can be answered by means of the key quantities already mentioned, i.e., the order parameter of seismicity and the entropy change of seismicity under time reversal along with their fluctuations. The explanation of the experimental findings identified before major EQs is given in a unified way on the basis of a physical model already proposed in the 1980s.

Spin stiffness, spectral weight, and Landau damping of magnons in metallic spiral magnets

We analyze the properties of magnons in metallic electron systems with spiral magnetic order. Our analysis is based on the random phase approximation for the susceptibilities of tight binding electrons with a local Hubbard interaction in two or three dimensions. We identify three magnon branches from poles in the susceptibilities, one associated with in-plane, the other two associated with out-of-plane fluctuations of the spiral order parameter. We derive general expressions for the spin stiffnesses and the spectral weights of the magnon modes, from which also the magnon velocities can be obtained. Moreover, we determine the size of the decay rates of the magnons due to Landau damping. While the decay rate of the in-plane mode is of the order of its excitation energy, the decay rate of the out-of-plane mode is smaller so that these modes are asymptotically stable excitations even in the presence of Landau damping.

Thermophysical behavior of mercury-lead liquid alloy

Thermophysical properties of compound forming binary liquid mercury-lead alloy at temperature 600 K have been reported as a function of concentration by considering HgPb2 complex using different modelling equations. The thermodynamic properties such as the Gibbs free energy, enthalpy of mixing, chemical activity of each component, and microscopic properties such as concentration fluctuation in long-wavelength limit and Warren-Cowley short range order parameter of the alloy are studied by quasi-chemical approximation. This research paper places additional emphasis on the interaction energy parameters between the atoms of the alloy. The theoretical and experimental data are compared to determine the model’s validity. Compound formation model, statistical mechanical technique, and improved derivation of the Butler equation have all been used to investigate surface tension. The alloy’s viscosity is investigated using the Kozlov-Ronanov-Petrov equation, the Kaptay equation, and the Budai-Benko-Kaptay model. The study depicts a weak interaction of the alloy, and the theoretical thermodynamic data derived at 600 K are in good agreement with the experimental results. The surface tension is slightly different in the compound formation model than in the statistical mechanical approach and the Butler equation at greater bulk concentrations of lead. The estimated viscosities in each of the three models are substantially identical.

Extremely low-energy collective modes in a quasi-one-dimensional topological system

We have investigated the quasiparticle dynamics and collective excitations in the quasi-one-dimensional material ZrTe5 using ultrafast optical pump-probe spectroscopy. Our time-domain results reveal two coherent oscillations having extremely low energies of ħω1 ∼0.33 meV (0.08 THz) and ħω2 ∼1.9 meV (0.45 THz), which are softened as the temperature approaches two different critical temperatures (∼54 K and ∼135 K). We attribute these two collective excitations to the amplitude mode of photoinduced dynamic charge density waves in ZrTe5 with tremendously small nesting wave vectors. Furthermore, a peculiar quasiparticle decay process associated with the ħω2 mode with a timescale of ∼1–2 ps is found below the transition temperature T* (∼135 K). Our findings provide pivotal information for studying the fluctuating order parameters and their associated quasiparticle dynamics in various low-dimensional topological systems and other materials.

Analytic form of a two-dimensional critical distribution.

This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin-wave model, or width fluctuations of a two-dimensional Edwards-Wilkinson interface. It is shown that the characteristic function of the distribution can be expressed exactly as a gamma function quotient, while a Charlier series, using the convolution of two Gumbel distributions as the kernel, converges to the exact result over a restricted domain. These results can also be extended to calculate the temperature dependence of the distribution and give an insight into the origin of Gumbel-like distributions in steady-state and equilibrium quantities that are not extreme values.

Interplay of interactions and disorder at the charge density wave transition of two-dimensional Dirac semimetals

We consider the effects of weak quenched fermionic disorder on the quantum-phase transition between the Dirac semimetal and charge density wave (CDW) insulator in two spatial dimensions. The symmetry breaking transition is described by the Gross-Neveu-Yukawa (GNY) theory of Dirac fermions coupled to an Ising order parameter field. Treating the disorder using the replica method, we consider chemical potential, vector potential (gauge), and random mass disorders, which all arise from nonmagnetic charged impurities. We self-consistently account for the Landau damping of long-wavelength order-parameter fluctuations by using the nonperturbative RPA resummation of fermion loops and compute the renormalization-group (RG) flow to leading order in the disorder strength and $1/N$ ($N$ the number of Dirac fermion flavors). We find two fixed points, the clean GNY critical point, which is stable against weak disorder, and a dirty GNY multicritical point, at which the chemical potential disorder is finite and the other forms of disorder are irrelevant. We investigate the scaling of physical observables at this finite-disorder multicritical point which breaks Lorentz invariance and gives rise to distinct non-Fermi liquid behavior.

Fermi arcs and pseudogap phase in a minimal microscopic model of d -wave superconductivity

We show conclusively that a pseudogap state can arise at $T > T_c$, for reasonable pairing interaction strength, from order parameter fluctuations in a two dimensional minimal model of $d$-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest neighbor interaction and establish our result using a combination of cluster based Monte Carlo for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\sim 160 \times 160$ allows two major conclusions: (i)~at $T < T_c$, despite the presence of thermal phase fluctuations the superconductor has only nodal Fermi points while all non nodal points on the normal state Fermi surface show a two peak spectral function with a dip at $\omega =0$, and (ii)~for $T > T_c$ the Fermi points develops into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature $T^* > T_c$. We show the variation of $T_c$ and $T^*$ with coupling strength and provide detailed spectral results at a coupling where $T^* \sim 1.5T_c$.