Dynamic Critical Properties Research Articles

Unveiling the similarities and dissimilarities between dynamic and thermodynamic phase transitions in a magnetic binary alloy system: a Monte Carlo study

Being inspired by the results of recent experimental work ‘Phys. Rev. E 102 022 804’, we perform a series of Monte Carlo simulations to investigate the dynamic critical properties of a binary magnetic alloy system composed of two different components with different spin moments with the chemical formula . In the first part of the work, we concentrate our attention on the similarities between dynamic critical behavior and thermodynamic phase transition properties of the model. Finite-size scaling analyses suggest that the proposed binary alloy model exhibits 2D Ising universality class. In the second part, we examine the dynamic critical behavior in the presence of a magnetic bias field for which a metamagnetic sideband behavior originates in dynamic susceptibility curves. Our results yield that these metamagnetic anomalies survive for a wide range of magnetic atom concentration p A , and the strength of the anomalies observed in the field-dependent dynamic susceptibility varies very slowly with the T/T c ratio of the binary magnetic alloy.

Quantum Zeno effect and the many-body entanglement transition

We introduce and explore a one-dimensional "hybrid" quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a "quantum Zeno phase" where strong measurements suppress the entanglement growth to saturate in an area-law. Extensive numerical simulations of the quantum trajectories of the many-particle wavefunctions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable "weak measurement phase" that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a novel continuous quantum dynamical phase transition between the "weak measurement phase" and the "quantum Zeno phase", driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this novel quantum entanglement transition are accessed.

The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions

We investigate the dynamics of the randomly pinned Fredrickson-Andersen model on the Bethe lattice. We find a line of random pinning dynamical transitions whose dynamical critical properties are in the same universality class of the A2 and A3 transitions of the mode coupling theory. The A3 behavior appears at the terminal point, where the relaxation becomes logarithmic and the relaxation time diverges exponentially. We explain the critical behavior in terms of self-induced disorder and avalanches, strengthening the relationship discussed in recent works between glassy dynamics and random field Ising model.

Ferroic superglasses: Polar nanoregions in relaxor ferroelectric PMN versus CoFe superspins in a discontinuous multilayer

Superdipolar glass properties of polar nanoregions (PNRs) in relaxor ferroelectric $\mathrm{PbM}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}{\mathrm{O}}_{3}$ (PMN) are compared to those of ferromagnetic nanoparticles (FNPs) in the superspin glass ${[\mathrm{C}{\mathrm{o}}_{80}\mathrm{F}{\mathrm{e}}_{20}(0.9\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}(3\phantom{\rule{0.16em}{0ex}}\mathrm{nm})]}_{10}$. Both the dynamic critical properties at $Tg{T}_{g}$ and nonergodicity phenomena at $Tl{T}_{g}$ are comparable, but this does not apply to their polydispersivity at $T\ensuremath{\le}{T}_{g}$. Due to the quenched random size and position distribution of the FNP, the superspin glass exhibits standard Cole-Cole broadening of the spectrum of relaxation frequencies at all temperatures. Contrastingly, the relaxation spectrum of the PNRs in PMN is subject to a crossover from Lacroix-B\'en\'e to Cole-Davidson statistics on cooling toward ${T}_{g}$. Surprisingly, it becomes replaced by relaxation and creeplike domain-wall dynamics below ${T}_{g}$ as a consequence of volume percolation of the PNR at ${T}_{g}$ and formation of a ferroelectric microdomain state under the simultaneous control by quenched random electric fields and the softening ferroelectric ${F}_{1u}$ lattice mode.

The dynamic critical properties of the spin-2 Ising model on a bilayer square lattice

The spin-2 Ising model is investigated for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the two-layer square lattice by using the Glauber-type stochastic dynamics. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip. By employing the Master equation and Glauber transition rates, the dynamic equations of the system are obtained. These equations are solved by using the numerical methods. First, we investigate the average order parameters as a function of the time to find the phases in the system. Then, the temperature-dependence of the dynamic order parameters is examined to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are presented on the different planes. According to the values of the system parameters, a variety of dynamic critical points such as tricritical point, triple point, quadruple point, critical end point, double critical end point, zero-temperature critical point, multicritical point and tetracritical point are obtained. The reentrant behavior is seen in the system for the AFM/AFM interaction. Finally, we also investigate the influence of the oscillating field frequency on the dynamic phase diagrams in detail.

Dynamical phase transition in the open Dicke model

The Dicke model with a weak dissipation channel is realized by coupling a Bose-Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp-Lieb-Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions.

Dynamical mean field theory phase-space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.

Finite-time scaling via linear driving

We propose systematic finite-time scaling and show that it can be used to determine both static and dynamic critical properties. The controllable finite time scale that affects the scaling of a system and that serves as an analogue of the system size in finite-size scaling is achieved simply but generally by manipulating the dynamics with an external field varying linearly with time. An analytic renormalization-group theory is developed to justify the scaling. Monte Carlo simulation results for two- and three-dimensional Ising models agree with existing ones and confirm the scaling and the method.

Nonequilibrium critical relaxation of the order parameter and energy in the two-dimensional ferromagnetic Potts model

The static and dynamic critical properties of the ferromagnetic q -state Potts models on a square lattice with q=2 and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are investigated, from which static and dynamic critical exponents can be obtained. We find that the static exponents thus obtained from the relaxation of the order parameter and energy together with the second moments of the order parameter exhibit a close agreement with the exact exponents, especially for the case of the q=2 (Ising) model, when care is taken in the choice of the initial states for the relaxation of the second moments. As for the case of q=3 , the estimates for the static exponents become less accurate, but still exhibit reasonable agreement with the exactly known static exponents. The dynamic critical exponent for the q=2 (Ising) model is estimated from the relaxation of the second moments of the order parameter with mixed initial conditions to give z(q=2) approximately 2.1668(19) .

Model C critical dynamics of random anisotropy magnets

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets, the structural disorder is present in the form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However the structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching the asymptotic regime.

Static and dynamic critical properties of the quasi-two-dimensional antiferromagnetMnPS3

A comprehensive study of the static and dynamic critical properties of the quasi-two-dimensional antiferromagnet MnPS3 is presented. The relatively large spin S=5/2 of the Mn ions ensure predominantly classical behavior, and the compound is believed to be a good example of a Heisenberg-type system on a honeycomb lattice. The sample has been measured using a variety of neutron-scattering techniques and instrumentation. The results are compared to the three-dimensional (3D) Heisenberg model, the two-dimensional classical O(3) rotator model, the two-dimensional XY model, and the related two-dimensional anisotropic Heisenberg model. The critical properties appear to be best described by the last model almost entirely over the measured temperature range, except just below the Neel temperature where the critical behavior seems to be 3D. There are some discrepancies, particularly in the rescaling of the spin stiffness and the energy widths of the structure factor. A possible explanation for the XY-like behavior is offered, involving the magnetic anisotropy in the system and its influence on the Hamiltonian.

Phase transition in fiber bundle models with recursive dynamics.

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterized by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive exact expressions for the order parameter, the susceptibility to changes in the initial applied stress, and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

Monte Carlo simulation of an Ising model on a Sierpiński carpet

We study by Monte Carlo simulation the equilibrium and dynamical critical properties of fractal lattices with noninteger Hausdorff dimension. These lattices are known to be good candidates to bridge the gap between integer dimensions. Focusing on the Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski carpet with Ising spins, we are able to obtain the critical exponents that are to be compared to the predictions of the renormalization group. We point out that the use of finite-size scaling is forbidden for fractal lattices. This might explain the difference from the exponents obtained in previous studies.

Dynamic critical properties of the vortex-glass transition derived from angular-dependent properties ofLa2−xSrxCuO4films

We present resistivity data on a high-quality La$_{2-x}$Sr$_{x}$CuO$_{4-\delta}$ film measured in a magnetic field of 1 T applied at an angle $\delta$ to the c axis. Using these data, the influence of the orientation of the magnetic field and the effective mass anisotropy on the vortex-glass transition can be studied. The variation of $\delta$ for a fixed magnitude of the magnetic field allows us to investigate the critical properties of interest, including the 2D-to-3D crossover and the 3D vortex glass-to-fluid transition, as the temperature is decreased. The data are well described by the scaling theory for the d.c. resistivity of an anisotropic superconductor in a magnetic field applied at an angle $\delta$ to the c axis. This scaling includes the critical properties close to and at the vortex-glass transition. The main results include (i) evidence of a Kosterlitz-Thouless transition in zero field, and (ii) a 2D-to-3D crossover at H=1 T as the temperature is decreased below the zero-field transition temperature, leading to the vortex fluid-to-vortex glass transition in D = 3 characterized by the dynamic critical exponent $z\approx 5.7$.

Static and dynamic critical properties of 3D systems with long-range correlated quenched defects

A field-theoretic description of static and purely relaxational dynamic critical behaviour of systems with quenched defects obeying power law correlations ~|x|-a for large separations x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2 a3, a renormalization analysis of the scaling functions in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by a double ,-expansion. The static and dynamic critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.

Driven diffusion of vector fields

A model for the diffusion of vector fields driven by external forces is proposed. Using the renormalization group and the $\epsilon$-expansion, the dynamical critical properties of the model with gaussian noise for dimensions below the critical dimension are investigated and new transport universality classes are obtained.

Early-time critical dynamics of lattices of coupled chaotic maps

The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is placed on obtaining accurate estimates of the dynamic critical exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ and $z$. The critical points of five different models are investigated, varying the mode of update, the coupling, and the local map. Our results suggest that the nature of update is a relevant parameter for dynamic universality classes of extended dynamical systems, generalizing results obtained previously for the static properties. They also indicate that the universality observed for the static properties of Ising-like transitions of synchronously updated systems does not hold for their dynamic critical properties.

Critical behavior of O(n)-symmetric systems with reversible mode-coupling terms: Stability against detailed-balance violation

We investigate nonequilibrium critical properties of O(n)-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy (SSS) is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures ${\mathrm{T}}_{\mathrm{S}}$ and ${\mathrm{T}}_{\mathrm{M}}$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first fixed point corresponds to \ensuremath{\Theta}=${\mathrm{T}}_{\mathrm{S}}$/${\mathrm{T}}_{\mathrm{M}}$=\ensuremath{\infty} and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at \ensuremath{\Theta}=0 and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent z=d/2 equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.

Solid on solid on fluid lattices

We perform simulations of a discrete gaussian solid on solid (DGSOS) model on dynamical ø 3 graphs, which is equivalent to coupling the model to 2d quantum gravity, using the cluster algorithms recently developed by Evertz et al. for use on fixed lattices. We find evidence from the growth of the width-squared in the rough phase of KT-like behaviour, which is consistent with theoretical expectations. We also investigate the cluster statistics, dynamical critical exponent and lattice properties, and compare these with the dual XY model.

MODE-COUPLING APPROACH TO THE SPIN DYNAMICS OF EUROPIUM COMPOUNDS

The results of a numerical solution of the mode-coupling equations for EuO and EuS taking into account the microscopical properties of the compounds are presented. Good agreement with the available neutron scattering data is found and predictions for further experiments on EuS are given. The results of high resolution neutron scattering experiments on insulating ferromagnetic Europium compounds EuO and EuS appeared in literature in recent years [I-41. The particular attention devoted to such compounds, is due to the fact that already in the earlier neutron scattering comprehensive investigation on E n 0 and EuS [I] it was shown that the magnetic behaviour of these systems is very well described by a simple isotropic Heisenberg exchange interaction. The availability of experimental data at and above the ordering temperature Tc has encouraged a renewal of theoretical studies on critical and paramagnetic spin fluctuations in Heisenberg ferromagnets. The most successful theories appear to be those ones based on Renormalization Group (RG) or on the mode-coupling approximation. RG techniques constitute a well established method to study the static and dynamic critical properties of a system; they allow to evaluate critical exponents as well as universal functions which characterize the critical behaviour. Very recently an attempt has been made to extend RG calculations to temperatures above Tc [5], but some problems persist to make possible a quantitative comparison with experimental data. The mode coupling approximation, in spite of its heuristic character, has revealed very useful in many problems of condensed matter physics [6]. For pure Heisenberg magnets, for example, it gives for the critical dynamical scaling ex,ponent z the value z = 171, in a agreement with 2 the experiments. Moreover it has been shown very recently [8] that by taking into account the dipolar macroscopic interaction, the mode-coupling theory can be able to interpret the unexpected simple exponential decay obtained in neutron spin-echo experiment on EuO at T = Tc and very small wave vector [4], which remained until now inexplicable. However the mode-coupling theory appears also suitable to investigate the dynamical behaviour of ferromagnetic systems in all the paramagnetic region and throughout the Brillouin Zone. In this paper we present the results of a numerical solution of the modecoupling equations for EuO and EuS taking into account the microscopical features of these compounds. This allows to show some distinctive characters which distinguish EuS from EuO that cannot be accounted by previous approximate solutions, which were limited to simple cubic nearest neighbours interaction [7] or confined to the continuum limit [6]. Europium compounds can be described by a Heisenberg exchange hamiltonian: I for an FCC lattice of magnetic ions with S = -. The 2 experiments [I] have shown that the interaction is restricted to nearest neighbours (J1) and next nearest neighbours (Jz ) . For EuO: J1 = 1.22' K , J2 = 0.25' K and a = 5.12 A; for EuS: J1 = 0.48' K , J2 = -0.24' K and a = 5.95 A, a being the lattice constant. The final result given by the mode-coupling theory is the following integr~differential equation: for the relaxation function Fq ( t ) , whose Fourier Transform is related to the measured scattering function S (q, w ) by the relation: W (q' W, = 1 exp (-v/KBT) .x (4) F, ( w ) . (3) Not with standing formal differences in the various derivations, behind equation (2) is the following fundamental approximation: correlation and relaxation functions among more than two spin operators have been decoupled. Equation (2) is only one of the forms in which this equation is obtained, however all such forms are equivalent if we use for the static susceptibility that one given by the spherical model: Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888720 C8 1572 JOURNAL DE PHYSIQUE This susceptibility turns out to be compatible with the dynamical equation (2). The temperature dependent parameter X appearing in equation (4) can be evaluated by using the sum rule: (I/N) C T X ~ = s(S + 1) /3.