Dynamic Order Parameter Research Articles

Dynamic magnetic properties and magnetocaloric effect of a nanotube encapsulated with X36

Abstract Using Monte Carlo simulation, the dynamic magnetic properties and magnetocaloric effect of a mixed-spin (3/2, 2) single-walled nanotube encapsulated with X36 was studied, where X denotes the magnetic atom. The effects of intrinsic parameters on dynamic order parameters, magnetic susceptibility, internal energy, and specific heat were considered. The phase diagrams were obtained. The results indicate that the critical temperature can be increased by decreasing the absolute values of the anisotropies (D a , D b ), increasing the exchange couplings (|J ab |, J bb ), and decreasing the amplitude h 0 and the period τ of the external magnetic field. And under the influence of these parameters, the magnetocaloric effect is generated.

Theoretical and Numerical Modeling of Optical Switching of Epitaxial Nanostructures Based on Iron-Garnet Films

The paper presents a theoretical analysis of magnetization switching in a gadolinium ferrite garnet film due to the demagnetizing effect of a femtosecond laser pulse. Using the Lagrange formalism for a two-sublattice ferrimagnet, the effective Lagrangian, thermodynamic potential, and Rayleigh dissipative function are obtained. The phase diagram of the ferrite film is analyzed, and the main states of the system are identified. Magnetization switching diagrams and trajectories of the order parameter dynamics of the magnet are constructed. The ranges of magnetic fields, temperatures, and demagnetization values for the most efficient magnetization switching are analyzed.

Dynamics of finite width Kernel and prediction fluctuations in mean field neural networks*

Abstract We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O ( 1 / width ) fluctuations of the dynamical mean field theory order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. We find that once the mean field/µP parameterization is adopted, the leading finite size effect on the dynamics is to introduce initialization variance in the predictions and feature kernels of the networks. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently. In two layer networks, we show how feature learning can dynamically reduce the variance of the final tangent kernel and final network predictions. We also show how initialization variance can slow down online learning in wide but finite networks. In deeper networks, kernel variance can dramatically accumulate through subsequent layers at large feature learning strengths, but feature learning continues to improve the signal-to-noise ratio of the feature kernels. In discrete time, we demonstrate that large learning rate phenomena such as edge of stability effects can be well captured by infinite width dynamics and that initialization variance can decrease dynamically. For convolutional neural networks trained on CIFAR-10, we empirically find significant corrections to both the bias and variance of network dynamics due to finite width.

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids.

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

Flux-quench induced dynamical quantum phase transitions in an extended XY spin-chain

Dynamical quantum phase transitions (DQPTs) induced by flux-quench in an extended transversed XY spin-chain have been investigated in this paper. We discussed the conditions for the appearance of DQPTs, and the different regions of the flux quench restricted by strength of transverse field were given. The Loschmidt echo, rate function, geometric phase, as well as dynamical topological order parameter (DTOP) have been calculated, which consistently verified the emergence of DQPTs.

Emergent symmetry in TbTe3revealed by ultrafast reflectivity under anisotropic strain.

We report ultrafast reflectivity measurements of the dynamics of the order parameter of the charge density wave (CDW) in TbTe3under anisotropic strain. We observe an increase in the frequency of the amplitude mode with increasing tensile strain along thea-axis (which drives the lattice intoa > c, withaandcthe lattice constants), and similar behavior for tensile strain alongc(c > a). This suggests that both strains stabilize the corresponding CDW order and further support the near equivalence of the CDW phases oriented ina- andc-axis, in spite of the orthorhombic space group. The results were analyzed within the time-dependent Ginzburg-Landau framework, which agrees well with the reflectivity dynamics. Our study presents an ultrafast approach to assess the stability of phases and order parameter dynamics in strained systems.

Nonequilibrium tricritical behavior in anisotropic XY ferromagnet driven by elliptically polarized propagating magnetic field wave

The three-dimensional anisotropic XY ferromagnet, driven by an elliptically polarized propagating magnetic field wave, has been extensively investigated by Monte Carlo simulation with the Metropolis single spin flip algorithm. Both the effects of the bilinear exchange type and the single-site anisotropies are thoroughly investigated. The time-averaged magnetization (over the complete cycle of the elliptically polarized propagating magnetic field wave) components play the role of the dynamic order parameter. For a fixed set of values of the strength of anisotropy and the field amplitudes, the system has been found to get dynamically ordered at a pseudocritical temperature. The pseudocritical temperature of such a dynamic nonequilibrium phase transition has been found to depend both on the strength of anisotropy and the amplitudes of the elliptically polarized propagating magnetic field wave. A comprehensive phase diagram is represented here in the form of an image plot of the pseudocritical temperature in the plane formed by the strength of anisotropy and field amplitudes. Interestingly, this nonequilibrium phase transition has been found to be discontinuous (first order) for higher values of the field amplitude. On the other hand, the continuous (second order) transition has been noticed for lower values of the field amplitude. Such an interesting nonequilibrium tricritical behavior has been observed in driven XY ferromagnet. The order of such a nonequilibrium phase transition has been confirmed by the thermal variation (near the transition) of the statistical distribution of the order parameter and by the thermal variation of the fourth-order Binder cumulant. In the plane formed by field amplitude and anisotropy, a tricritical line has been shown as the accompanying (and complementary) phase diagram. The dependence of the pseudocritical temperature, on the frequency and wavelength of the elliptically polarized propagating magnetic field wave, has also been reported.

Metamagnetic anomalies in the kinetic Ashkin–Teller model

This study investigates the metamagnetic anomaly in the Ashkin–Teller spin-1/2 model in a ferromagnetic state, utilizing dynamic mean-field theory on a cubic lattice from a stochastic theory. We analyze instantaneous magnetizations over time, dynamic order parameters, and magnetic susceptibilities concerning the constant bias field, as well as examining dynamic phase diagrams. Our observations reveal that dynamic phase transitions occur at specific points of the constant bias field, where instantaneous magnetization transitions from oscillating between negative and positive states to a strictly positive state. We also observe a narrow region in the dynamic phase diagram between phase transitions of different order parameters of the model, for some conditions among the couplings of these order parameters. These results contribute to an understanding of the dynamic behavior of the spin-1/2 AT model under ferromagnetic conditions, providing interesting insights into phase transitions and the metamagnetic anomaly.

Photo-induced collective charge-density-wave dynamics in bulk 1T-VSe2

We investigated temperature (T) and excitation density dependent ultrafast near-infrared (NIR) transient reflectivity dynamics in the charge density wave (CDW) phases of bulk layered 1T-VSe2 using NIR and visible excitations. The data reveal fingerprints of conventional non-adiabatic CDW collective dynamics with rather fast electronic order parameter dynamics showing sub-picosecond suppression and recovery. The slower T-dependent 100-ps dynamics indicates rather isotropic heat transport dominated by the lattice degrees of freedom.

Ordering kinetics in the active Ising model.

We undertake a numerical study of the ordering kinetics in the two-dimensional (2D) active Ising model (AIM), a discrete flocking model with a conserved density field coupled to a nonconserved magnetization field. We find that for a quench into the liquid-gas coexistence region and in the ordered liquid region, the characteristic length scale of both the density and magnetization domains follows the Lifshitz-Cahn-Allen growth law, R(t)∼t^{1/2}, consistent with the growth law of passive systems with scalar order parameter and nonconserved dynamics. The system morphology is analyzed with the two-point correlation function and its Fourier transform, the structure factor, which conforms to the well-known Porod's law, a manifestation of the coarsening of compact domains with smooth boundaries. We also find the domain growth exponent unaffected by different noise strengths and self-propulsion velocities of the active particles. However, transverse diffusion is found to play the most significant role in the growth kinetics of the AIM. We extract the same growth exponent by solving the hydrodynamic equationsof the AIM.

Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems.

By utilizing biorthogonal bases, we develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of the previously overlooked associated state, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues and naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a 1/2 change of dynamical topological order parameter in biorthogonal bases is observed which is not shown in self-normal bases. Furthermore, we discover that the periodicity of biorthogonal dynamical quantum phase transitions depends on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.

Nanosecond Structural Dynamics during Electrical Melting of Charge Density Waves in 1T-TaS_{2}.

Electrical control of charge density waves has been of immense interest, as the strong underlying electron-lattice interactions potentially open new, efficient pathways for manipulating their ordering and, consequently, their electronic properties. However, the transition mechanisms are often unclear as electric field, current, carrier injection, heat, and strain can all contribute and play varying roles across length scales and timescales. Here, we provide insight on how electrical stimulation melts the room temperature charge density wave order in 1T-TaS_{2} by visualizing the atomic and mesoscopic structural dynamics from quasi-static to nanosecond pulsed melting. Using a newly developed ultrafast electron microscope setup with electrical stimulation, we reveal the order and strain dynamics during voltage pulses as short as 20ns. The order parameter dynamics across a range of pulse amplitudes and durations support a thermally driven mechanism even for fields as high as 19 kV cm^{-1}. In addition, time-resolved imaging reveals a heterogeneous, mesoscopic strain response across the flake, including MHz-scale acoustic resonances that emerge during sufficiently short pulsed excitation which may modulate the order. These results suggest that metallic charge density wave phases like studied here may be more robust to electronic switching pathways than insulating ones, motivating further investigations at higher fields and currents in this and other related systems.

Verification of scaling behavior near dynamic phase transitions for nonantisymmetric field sequences.

We investigate the scaling behavior of the magnetic dynamic order parameter Q in the vicinity of the dynamic phase transition (DPT) in the presence of temporal field sequences H(t) that are periodic with period P but lack half-wave antisymmetry. We verify by means of mean-field calculations that the scaling of Q is preserved in the vicinity of the second-order phase transition if one defines a suitable generalized conjugate field H^{*} that reestablishes the proper time-reversal symmetry. For the purpose of our quantitative data analysis, we employ the dynamic equivalent of the Arrott-Noakes equation of state, which allows for a simultaneous scaling analysis of the period P and the conjugate-field H^{*} dependence of Q. By doing so, we demonstrate that both the scaling behavior and universality are preserved, even if the dynamics is driven by a more general applied field sequence that lacks antisymmetry.

Re-order parameter of interacting thermodynamic magnets

Phase diagrams of materials are typically based on a static order parameter, but it faces challenges when distinguishing subtle phase changes, such as re-ordering. Here, we report a dynamic nonequilibrium order parameter termed re-order parameter to determine subtle phases and their transitions in interacting magnets. The dynamical precession of magnetization, so-called magnon, premises as a reliable re-order parameter of strong spin-orbit coupled magnets. We employ orthoferrites YFeO3 and its Mn-doped variations, where diverse magnetic phases, including canted antiferromagnetic (Γ4) and collinear antiferromagnetic (Γ1) states, have been well-established. Low-energy magnon uncovers the spin-orbit coupling-induced subtle magnetic structures, resulting in distinct terahertz emissions. The temporal and spectral parameters of magnon emission exhibit characteristics akin to BCS-type order parameters, constructing the magnetic phase diagram of Mn-doped YFeO3. This approach further reveals a concealed ferrimagnetic phase within the Γ1 state, underscoring its potential to search for hidden phases of materials, completing their phase diagrams.

Magnetic behaviour of a mixed-spin ising model on a two-dimensional square-octagon lattice in a dynamic magnetic field

The magnetic behaviours of a two-dimensional square-octagon lattice with mixed spin 5/2 and spin 1 magnetic atoms are investigated in a dynamic magnetic field using effective field theory with correlations. We studied the effects of exchange coupling, anisotropy, oscillating magnetic fields, and temperature on the dynamic magnetic and thermodynamic properties of the square-octagon lattice. The dynamic magnetisation, order parameters, susceptibility, internal energy, and phase diagram of the system were obtained. These results significantly contribute to our understanding of the dynamic magnetic properties of two-dimensional materials. The ability to manipulate and control magnetic behaviour in two dimensions holds promise for the creation of more efficient and versatile devices.

Dynamical order and many-body correlations in zebrafish show that three is a crowd

Zebrafish constitute a convenient laboratory–based biological system for studying collective behavior. It is possible to interpret a group of zebrafish as a system of interacting agents and to apply methods developed for the analysis of systems of active and even passive particles. Here, we consider the effect of group size. We focus on two– and many–body spatial correlations and dynamical order parameters to investigate the multistate behavior. For geometric reasons, the smallest group of fish which can exhibit this multistate behavior consisting of schooling, milling and swarming is three. We find that states exhibited by groups of three fish are similar to those of much larger groups, indicating that there is nothing more than a gradual change in weighting between the different states as the system size changes. Remarkably, when we consider small groups of fish sampled from a larger group, we find very little difference in the occupancy of the state with respect to isolated groups, nor is there much change in the spatial correlations between the fish. This indicates that fish interact predominantly with their nearest neighbors, perceiving the rest of the group as a fluctuating background. Therefore, the behavior of a crowd of fish is already apparent in groups of three fish.

Tracing the dynamics of superconducting order via transient terahertz third-harmonic generation.

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify nonequilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently, nonlinear THz third-harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here, we extend this idea to light-driven nonequilibrium states in superconducting La2-xSrxCuO4, establishing an optical pump-THz-THG drive protocol to access the transient superconducting order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional TH spectroscopy to disentangle the effects of optically excited quasiparticles from the pure order-parameter dynamics, which are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.

Dynamical onset of light-induced unconventional superconductivity—a Yukawa-Sachdev-Ye-Kitaev study

Using light irradiation to manipulate quantum materials has opened up avenues for transiently inducing superconductivity in some systems. Despite experimental confirmation across various compounds, the mechanism behind the dynamic formation of Cooper pairs remains highly debated, in part due to the strong electronic correlations at play, which pose challenges for theoretical investigations relying on perturbative or phenomenological approaches. Here, we investigate the dynamical onset of superconductivity in the strongly correlated, yet exactly solvable Yukawa-Sachdev-Ye-Kitaev model. Analyzing dynamical protocols motivated by theoretical mechanisms proposed for light-induced superconductivity, that is light-induced cooling and the dressing of Hamiltonian parameters, we investigate the exact relaxation resulting out of undercooling and interaction quenches. While, in contrast to BCS theory, it is not possible for superconductivity to emerge following interaction quenches across the superconducting phase transition, we find that the dynamical relaxation of undercooled states universally leads to superconductivity. Despite the strong correlations, the emerging order parameter dynamics are well captured by a coarse grained Ginzburg-Landau theory. Our study provides an integral stepping stone towards exploring light-induced superconductivity in strongly correlated systems in a theoretically controlled way.

Order parameter dynamics in complex systems: From models to data

Collective ordering behaviors are typical macroscopic manifestations embedded in complex systems and can be ubiquitously observed across various physical backgrounds. Elements in complex systems may self-organize via mutual or external couplings to achieve diverse spatiotemporal coordinations. The order parameter, as a powerful quantity in describing the transition to collective states, may emerge spontaneously from large numbers of degrees of freedom through competitions. In this minireview, we extensively discussed the collective dynamics of complex systems from the viewpoint of order-parameter dynamics. A synergetic theory is adopted as the foundation of order-parameter dynamics, and it focuses on the self-organization and collective behaviors of complex systems. At the onset of macroscopic transitions, slow modes are distinguished from fast modes and act as order parameters, whose evolution can be established in terms of the slaving principle. We explore order-parameter dynamics in both model-based and data-based scenarios. For situations where microscopic dynamics modeling is available, as prototype examples, synchronization of coupled phase oscillators, chimera states, and neuron network dynamics are analytically studied, and the order-parameter dynamics is constructed in terms of reduction procedures such as the Ott–Antonsen ansatz, the Lorentz ansatz, and so on. For complicated systems highly challenging to be well modeled, we proposed the eigen-microstate approach (EMP) to reconstruct the macroscopic order-parameter dynamics, where the spatiotemporal evolution brought by big data can be well decomposed into eigenmodes, and the macroscopic collective behavior can be traced by Bose–Einstein condensation-like transitions and the emergence of dominant eigenmodes. The EMP is successfully applied to some typical examples, such as phase transitions in the Ising model, climate dynamics in earth systems, fluctuation patterns in stock markets, and collective motion in living systems.

Microscopic Cutoff Dependence of an Entropic Force in Interface Propagation of Stochastic Order Parameter Dynamics.

The steady propagation of a (d-1)-dimensional planer interface in d-dimensional space is studied by analyzing mesoscopic nonconserved order parameter dynamics with two local minima under the influence of thermal noise. In this analysis, an entropic force generating interface propagation is formulated using a perturbation method. It is found that the entropic force singularly depends on an ultraviolet cutoff when d≥2. The theoretical calculation is confirmed by numerical simulations with d=2. The result means that an experimental measurement of the entropic force provides an estimation of the microscopic cutoff of the mesoscopic description.