Tricritical Behavior Research Articles

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.

Thermodynamically consistent flocking: from discontinuous to continuous transitions

We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C, and that it generically exhibits tricritical behavior. Self-propulsion has a non-perturbative effect on the phase diagram, yielding novel phase behaviors depending on the type of aligning interactions. For aligning interaction that increase monotonically with the density, the tricritical point diverges to infinite density reproducing the standard scenario of a discontinuous flocking transition accompanied by traveling bands. In contrast, for models where the aligning interaction is non-monotonic in density, the system can exhibit either (the nonequilibrium counterpart of) an azeotropic point, associated with a continuous flocking transition, or a state with counterpropagating bands.

Microstructure, magnetocaloric effect and near tricritical mean-field critical behavior of La0.67Ca0.33-xKxMnO3 porous nanospheres prepared by solvothermal method

In this study, La0.67Ca0.33-xKxMnO3 porous nanospheres with K+ replacing Ca2+ were prepared by the solvothermal method. The microstructures, surface valence, magnetic properties, magnetocaloric effect and critical parameters of magnetic phase transition were investigated. The structural characterization showed that the grain size of La0.67Ca0.33-xKxMnO3 exhibited an increasing and then decreasing trend with the increase of K+ doping. The magnetic testing of La0.67Ca0.33-xKxMnO3 revealed that K+ doping increased the phase transition temperature of the system and modified the magnetic interactions before and after the phase transition temperature. As a result, the critical behavior of the magnetic phase transition was affected with K+ doping. When x = 0.05 and 0.1, the critical behavior of samples exhibited similarities to the tricritical mean-field model. Furthermore, K+ doping enhanced the magnetic refrigeration ability of the system, with the maximum magnetic entropy reaching 5.99 J/kg K for K-0.05.

Indications for an alternative breaking of symmetry in fracture-induced electromagnetic emissions recorded prior to the 2023 Mw7.8 and Mw7.5 Turkey Earthquakes

Several evidence has been reported corroborating the view that the MHz band fracture-induced electromagnetic emissions (FEME), also known as fracture-induced electromagnetic radiation (FEMR), which are detected prior to shallow main earthquakes (EQs) of moment magnitude Mw>5.5 with epicenters on land or near coastline, can be studied in analogy to a Z(2) spin system undergoing a second-order phase transition. Specifically, by analyzing MHz FEME/FEMR time series recorded prior to several earthquakes in the past >20 years, information has been extracted about the organization to critical state, the critical state itself, as well as for the step-by-step development of the spontaneous symmetry breaking (SSB) phenomenon. Using the “method of critical fluctuations” (MCF) and a recently proposed method for the wavelet-based detection of scaling behavior in noisy experimental data, we identified for the first time a different way of breaking the symmetry embedded in the MHz FEME/FEMR time series recorded by the hELlenic Seismo-ElectroMagnetics Network (ELSEM-Net) prior to the devastating (Mw=7.8 and Mw=7.5) EQs that occurred in south-east Turkey on 06/02/2023. Particularly, after the achievement of the critical state, indications were found that, although the underlying system started to break the symmetry according to the second-order phase transition mechanism (through SSB), SSB was not completed. Instead, the system seems to have changed symmetry and presented indications that the break of symmetry was finally achieved according to the first-order phase transition mechanism. Specifically, after the incomplete SSB, it was found to present tricritical behavior, followed by indications of triple degeneration of the order parameter fixed-point. This change of behavior observed in the MHz FEME/FEMR is a puzzling phenomenon for several reasons, which are discussed in detail, whereas suggestions are expressed as a first attempt for the possible explanation of the new findings.

A revisit to the Ising model in a transverse and random magnetic field

In this article we consider a Hamiltonian representing the Ising model in a random transverse magnetic field (RTIM). We use mean field theory via Bogoliubov’s inequality to calculate the Gibbs free energy and the longitudinal (mz) and transverse (mx) magnetizations. We show a quantum phase transition at zero temperature, i.e. the magnetization mz goes to zero only due to the transverse magnetic field. The temperature behavior as a function of the transverse magnetic field is also shown for different values of the anisotropy parameter p, where no tricritical behavior is observed. The behavior of mz and mx as a function of temperature and transverse magnetic field have been plotted, showing that there is no tricritical behavior.

Study of the Mixed Spin Ising Nanowire with Random and Dilute Crystal Field

The mixed spin Ising nanowire with random and dilute crystal fields has been explored based on the finite cluster approximation. Much concern has been addressed in treating the effects of the randomness with two distribution types of the crystal field on the phase diagrams. It has been demonstrated that for a low random crystal field D marked by the fluctuation d, all transition lines are of second order and are not particularly sensitive to the fluctuation; whereas, for high values of D, the transition temperature depends on the fluctuation and may display tricritical points. Under the effect of the dilute crystal field, according to the surface shell coupling strength, the tricritical behavior occurs exclusively for higher values of the concentration p where a large majority of spins are influenced by the crystal field. All these behaviors have been confirmed by examination of magnetizations.

Tricritical behavior in epidemic dynamics with vaccination

We scrutinize the phenomenology arising from a minimal vaccination-epidemic (MVE) dynamics using three methods: mean-field approach, Monte Carlo simulations, and finite-size scaling analysis. The mean-field formulation reveals that the MVE model exhibits either a continuous or a discontinuous active-to-absorbing phase transition, accompanied by bistability and a tricritical point. However, on square lattices, we detect no signs of bistability, and we disclose that the active-to-absorbing state transition has a scaling invariance and critical exponents compatible with the continuous transition of the directed percolation universality class. Additionally, our findings indicate that the tricritical and crossover behaviors of the MVE dynamics belong to the universality class of mean-field tricritical directed percolation.

Tricritical Behavior in Dynamical Phase Transitions.

We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and second-order bias-induced phase transition curves at two tricritical points. We formulate a simple, general criterion for its appearance and derive an exact Landau theory for the tricritical behavior. The scenario is demonstrated in three examples: the simple symmetric exclusion process biased by an activity-related structural observable; the Katz-Lebowitz-Spohn lattice gas model biased by its current; and in an active lattice gas biased by its entropy production.

Unusually large magnetic moment and tricritical behavior of the CMR compound NaCr2O4 revealed with high resolution neutron diffraction and SR

The mixed valence Cr3+/Cr4+ compound NaCr2O4, hosts a plethora of unconventional electronic properties. In the present study, muon spin rotation/relaxation (SR) and high-resolution time-of-flight neutron powder diffraction measurements were carried out on high-quality samples to clarify the complex magnetic ground state of this unique material. We identified a commensurate canted antiferromagnetic order (C-AFM) with a canting angle of the Cr spin axial vector equal to , and an estimated Cr moment . Such an unusually large value of is compatible with the existence of high-spin Cr sites created by the presence of an unconventional negative charge transfer state in NaCr2O4. In addition to the C-AFM structure, a novel magnetic supercell was also revealed. Such supercell display an incommensurate (IC)-AFM propagation vector (0 0 ), having a Cr moment . It is suggested that the C-AFM and IC-AFM modulations have two different electronic origins, being due to itinerant and localized contributions to the magnetic moment respectively. Finally, the direct measurement of the magnetic order parameter for the C-AFM structure provided a value of the critical exponent , suggesting a non conventional critical behavior for the magnetic phase transition in NaCr2O4.

Tricritical behavior of the smectic-hexatic phase transitions in binary mixtures using the landau mean field theory

ABSTRACT The smectic-hexatic phase transitions are studied by the Landau mean field theory in binary mixtures, particularly, THI-14 + MPR-6 liquid crystalline system. By considering the phase lines of SmA-Hex B, SmC-SmF (Hex F) and SmF-Hex B as the first order; SmA-SmC and SmC-SmF as the second order, in the presence of the two tricritical points (C-F-B and A-C-B), we calculate the T-X phase diagram of the binary mixture studied. The phase line equations obtained from the free energies of the smectic and hexatic phases, are fitted to the experimental data given in the literature. We find that the Landau mean field theory explains satisfactorily the observed T-X phase diagram for the smectic-hexatic transitions in the binary mixture of THI-14 + MPR-6.

Landau-de Gennes theory of the nematic to smectic—A phase transition under confinement conditions

We study the nature of the nematic to smectic-A phase transition under confinement conditions in the context of Landau-de Gennes theory. The effect of quenched disorder on the nematic to smectic-A transition temperature, order parameter, enthalpy, and thermal hysteresis are discussed followed by phase diagrams. The tricritical behavior of the nematic to smectic-A phase under confinement conditions is predicted.

Tricritical behavior in a neural model with excitatory and inhibitory units.

While the support for the relevance of critical dynamics to brain function is increasing, there is much less agreement on the exact nature of the advocated critical point. Thus, a considerable number of theoretical efforts are currently concentrated on which mechanisms and what type(s) of transition can be exhibited by neuronal network models. In that direction, the present work describes the effect of incorporating a fraction of inhibitory neurons on the collective dynamics. As we show, this results in the appearance of a tricritical point for highly connected networks and a nonzero fraction of inhibitory neurons.

Single-ion anisotropy as the source of anomalies in thermodynamic properties of magnetic spin-1/2 − 1 mixed systems on square and simple cubic lattices

The influence of the single-ion anisotropy on the thermodynamic properties of ferromagnetic as well as ferrimagnetic spin-1/2 − 1 mixed systems on the square and simple cubic lattice is investigated in the framework of the exactly solvable Ising-like models on the corresponding recursive lattices. The exact solutions of the models are present in the form of the explicit expressions for the free energy per site as the functions of the coordinates of the fixed points of the corresponding systems of recursion relations. The phase diagrams of the models are determined and the existence of compensation temperatures in the ferrimagnetic cases are discussed. The equations that drive the positions of the critical points are derived. The existence of the tricritical behavior in the three-dimensional system on the simple cubic lattice and its nonexistence in the case of the two-dimensional system on the square lattice is demonstrated. It is shown that the presence of the single-ion anisotropy can naturally lead to the emergence of the thermodynamic anomalies typical for frustrated magnetic systems even in unfrustrated ferromagnetic systems on studied bipartite lattices. First of all, the studied models exhibit the formation of strict residual-entropy hierarchies between the neighboring ground states of the system of three different ground states. It is also shown that due to this behavior of the entropy the specific heat capacity of the models exhibit anomalous (Schottky) behavior at low temperatures in the vicinity of the values of the anisotropy parameter, for which highly macroscopically degenerated single-point-like ground states are formed.

Metamagnetism and tricritical behavior in the Kondo lattice model

The phase diagram of the Kondo lattice model is explored around the ferromagnetic region, including an external magnetic field, and allowing the coexistence of ferromagnetism and Kondo effect ($\mathrm{FM}+\mathrm{K}$). Considering the combined effect of temperature and pressure, the evolution of the $\mathrm{FM}+\mathrm{K}$ phase yields a wing structure phase diagram with a tricritical point and a ferromagnetic quantum critical end point. The evolution of the spin-selective Kondo insulator phase, inside the coexistence region, introduces another critical end point. The results show a correspondence with the experimental phase diagram of heavy-fermion compounds, in particular, the ferromagnetic superconductor ${\mathrm{UGe}}_{2}$.

Tricritical fluctuations and elastic properties of the Ising antiferromagnet UIrSi3

Elastic constants, thermal expansion, magnetostriction, and heat capacity measurements were performed with and without applied magnetic field on a single crystal of ${\mathrm{UIrSi}}_{3}$. The elastic properties were interpreted within the theory of the strain-exchange effect. The exchange-striction model together with the Ising model for the behavior of magnetic localized $5f$ electrons and itinerant electrons of uranium correctly reproduces the main features of our magneto-acoustic experiments in ${\mathrm{UIrSi}}_{3}$. Data on thermal expansion and magnetostriction confirm the conclusion that the dominant contribution of the measured temperature and field change in the speed of sound comes from the change in the elastic modulus itself. Based on the analysis of heat capacity measurements in the magnetic field, we explain the significant anomalies at the second-order branch of the phase transition boundary as a manifestation of the tricritical fluctuations, dominating the region below the tricritical point. The outcome confirms the three-dimensional Ising model, at zero and low magnetic fields, with a crossover to the mean-field tricritical behavior at fields close to the tricritical point, where tricritical fluctuations dominate the temperature evolution of the given property.

Numerical evidence of Janssen-Oerding's prediction in a three-dimensional spin model far from equilibrium.

In 1994, Jansen and Oerding predicted an interesting anomalous tricritical dynamic behavior in three-dimensional models via renormalization group theory. However, we highlight the lack of literature about the computational verification of this universal behavior. Here, we use some tricks to capture the log corrections and the parameters predicted by these authors using the three-dimensional Blume-Capel model. We quantify the crossover phenomena by computing the critical exponents near the tricritical point. In addition, we also perform a more detailed study of the dynamic localization of the phase diagram via power-law optimization.

Effects of dilution in ionic liquid supercapacitors

Room-temperature ionic liquids (RTILs) are synthetic electrolytes that have a large electrochemical stability window, making them attractive candidates for electric double-layer capacitor (EDLC) applications. Due to their high viscosities and low ionic conductivities, RTILs are often diluted with organic solvent for practical use. We study the effects of dilution on the performance of RTIL EDLCs using a simple mean-field model. We find that dilution diminishes the unfavorable hysteresis that results from a spontaneous surface charge separation (SSCS). As a result, the RTIL concentration can be used to modulate the proximity to the SSCS transition, and maximize capacitance. The interplay between the concentration and the correlation strength gives rise to complex zero-potential phase behavior, including a tricritical point and a λ-line, very similar to the Blume-Capel dilute Ising model. Additionally, electrodes that are solvophilic aid in the prevention of SSCS by drawing solvent molecules to the electrode and displacing ions. Solvophilic electrodes give rise to a phase transition at finite potential where the surface charge rapidly increases with a small increase in potential, leading to a substantial increase in capacitance and energy storage.

Dynamic multicritical phase diagrams of the mixed spin (2, 5/2) Blume-Emery-Griffiths model with repulsive biquadratic coupling

We investigated the dynamic phase transitions (DPTs) in the mixed spin (2, 5/2) Blume-Emery Griffiths model with repulsive biquadratic interaction in the presence of a time-varying magnetic field. We used the path probability method to obtain the set of the dynamic equations. We numerically solved these dynamic equations to characterize the nature of first- and second-order phase transitions and to find the DPT temperatures as well as obtain the phases in the system. We constructed the dynamic phase diagrams (DPDs) in reduced temperature and amplitude of oscillating magnetic field plane. We observed that the DPDs display richer, complex and more topological various type of phase diagrams. In particular, DPDs exhibit the disordered phase, antiquadrupolar or staggered phase, six different ferrimagnetic phases, three different nonmagnetic phases, and numerous mixed phases. DPDs also display two dynamic tricritical points for only smaller values of crystal-field interactions, multiple critical end and double critical end points, one zero-temperature critical point, one inverse critical end point, and a quadruple point depending on interaction parameters. The system always shows the reentrant behaviors for the higher values of magnetic field amplitude, but it does not exhibit the dynamic tricritical behavior for higher values of crystal-field parameter.

Field-induced tricritical phenomenon and magnetic structures in magnetic Weyl semimetal candidate NdAlGe

Non-centrosymmetric NdAlGe is considered to be a candidate for magnetic Weyl semimetal in which the Weyl nodes can be moved by magnetization. Clarification of the magnetic structures and couplings in this system is thus crucial to understand its magnetic topological properties. In this work, we conduct a systematical study of magnetic properties and critical behaviors of single-crystal NdAlGe. Angle-dependent magnetization exhibits strong magnetic anisotropy along the c-axis and absolute isotropy in the ab-plane. The study of critical behavior with H∥c gives critical exponents β = 0.236(2), γ = 0.920(1), and δ = 4.966(1) at critical temperature T C = 5.2(2) K. Under the framework of the universality principle, M(T, H) curves are scaled into universality curves using these critical exponents, demonstrating reliability and self-consistency of the obtained exponents. The critical exponents of NdAlGe are close to the theoretical prediction of a tricritical mean-field model, indicating a field-induced tricritical behavior. Based on the scaling analysis, a H–T phase diagram for NdAlGe with H∥c is constructed, revealing a ground state with an up-up-down spin configuration. The phase diagram unveils multiple phases including up-up-down domains, up-up-down ordering state, polarized ferromagnetic (PFM), and paramagnetic (PM) phases, with a tricritical point (TCP) located at the intersection [T TCP = 5.27(1) K, H TCP = 30.1(3) kOe] of up-up-down, PFM, and PM phases. The multiple phases and magnetic structures imply a delicate competition and balance between variable interactions and couplings, laying a solid foundation for unveiling topological properties and critical phenomena in this system.

Phase diagrams and magnetisations of mixed spin nanoparticles with transverse field and crystal field

ABSTRACT Using the finite cluster approximation, we investigate the phase transitions of two mixed spin 2D-nanoparticles. The effects of the crystal field and the transverse field parameters on phase diagrams and magnetisations have received the most attention. In a certain range of surface shell coupling, the model exhibits a tricritical behavior when only a longitudinal crystal field is present. The reentrance behavior may occur when the core and shell transverse fields are introduced, and the tricritical behavior may persist for appropriate values of the system parameters.