Tricritical Point Research Articles

Minimizing the profligacy of searches with reset

We introduce the profligacy of a search process as a competition between its expected cost and the probability of finding the target. The arbiter of the competition is a parameter λ that represents how much a searcher invests into increasing the chance of success. Minimizing the profligacy with respect to the search strategy specifies the optimal search. We show that in the case of diffusion with stochastic resetting, the amount of resetting in the optimal strategy has a highly nontrivial dependence on model parameters resulting in classical continuous transitions, discontinuous transitions and tricritical points, as well as nonstandard discontinuous transitions exhibiting reentrant behavior and overhangs. Published by the American Physical Society 2024

Experimental Quantum Simulation of Multicriticality in Closed and Open Rabi Model.

Quantum multicriticality not only has fundamental research significance but also can promote the development of emerging quantum technologies, owing to its rich phase transition mechanisms and quantum resources. While theoretical studies have predicted the multicritical phenomena in the light-matter systems, the experimental demonstration remains elusive for the challenges of achieving the system's ground or steady states in strong coupling regimes. Here, by implementing the quantum adiabatic algorithm and the dissipative-system variational quantum algorithm on nuclear magnetic resonance quantum simulator, we successfully demonstrate the tricritical phenomena both in the closed and open systems described by the two-axis Rabi model. The experimental results clearly show that, beyond the decoherence effect, dissipation leads to the emergence of a novel multicritical phenomenon: it splits the first-order phase transition line of the closed Rabi model, and doubles the tricritical point. Our work provides a feasible technique for engineering the open quantum systems and opens a new avenue for exploring nonequilibrium many-body physics.

Crystal structure and magnetic properties of Yb2Pt2Pb under multi-extreme conditions

ABSTRACT Structural and magnetic properties of the Shastry-Sutherland material Yb2Pt2Pb were studied in single-crystalline form under pressures up to 10 GPa, magnetic fields up to 17 T, and temperatures down to 0.3 K. Surprisingly robust magnetic order is observed with the Néel temperature T N = 2.1 K stable up to 8.1 GPa. Indication of an additional magnetic phase formation can be traced in resistivity data for magnetic field along the c-axis exceeding the (pressure-dependent) metamagnetic transition. The related anomaly shifts to higher temperatures with increasing field, merging T N at the tricritical point. Experiments with μ0 H // [110] revealed the pressure stabilization of observed magnetic phases with respect to the magnetic field. The crystal-structure type is stable up to 10 GPa, without any sign of symmetry change, exhibiting moderate volume compressibility with bulk modulus B = 116(13) GPa, in good agreement with B = 118 GPa provided by the density functional theory.

Diversity of ultrafast spin dynamics near the tricritical point in a ferrimagnetic Gd/FeCo multilayer

Diversity of ultrafast spin dynamics near the tricritical point in a ferrimagnetic Gd/FeCo multilayer

Insight into electronic and magnetic properties of Ba2NiOsO6 double perovskite: A Monte Carlo study and a comparative investigation between TB-mBJ and GGA+U

The structural, electronic, and magnetic properties of the Ba2NiOsO6 double perovskite were comprehensively studied using density functional theory (DFT) and Monte Carlo simulations. Based on DFT calculations, we found that the double perovskite is stable in the ferromagnetic phase. The compound exhibited thermodynamic stability, confirmed by its negative formation energy and phonon spectrum. The electronic and magnetic properties were analyzed using various approximations, including the Generalized Gradient Approximation (GGA), modified Becke–Johnson approximation (mBJ), and Hubbard correction (GGA+U). The electronic profile indicated a metallic nature with GGA and a half-metallic nature with GGA+U and mBJ. The total magnetic moment was approximately 4 μB across all approximations. The Monte Carlo simulations revealed intriguing phenomena, such as a tri-critical point, second-order and first-order phase transitions, a reentrant phenomenon, and both simple and double hysteresis loops.

Phase transitions in rare-earth ferrimagnets with surface anisotropy near the magnetization compensation point

Theoretical model is proposed for calculating the phase H-T diagrams of a rare-earth ferrimagnet, considering the effects of each of the magnetic sublattices and surface anisotropy. Magnetic phase diagrams are numerically calculated. The presence of surface anisotropy leads to blurring of the second-order phase transition lines between the collinear and angular phases, displacement of the tricritical point, as well as the possibility of the formation of new phase transition lines.

Cylindrical Blume-Capel Nanotube with core/shell structure: compensation temperature and hysteresis loops

The critical, compensation and hysteresis behaviors of the Blume-Capel model with mixed spins SkS=±2,±1,0 and σiC=±3/2,±1/2 , on a cylindrical nanotube with core–shell structure were studied using the mean-field approximation based on the Gibbs-Bogoliubov inequality. The effects of the single-ion anisotropies and the exchange coupling on phase diagrams, magnetizations and hysteresis loops were investigated. The first-order and second-order phase transitions and critical end-point were found, therefore, the system does not give any tricritical point. Furthermore, the model’s results anticipate the presence of the compensation phenomena and multi-cycle hysteresis behaviors.

Magnetic and thermodynamic properties of mixed spin-3/2 and spin-3 Ising ferrimagnets on a 2D triangular lattice: Monte Carlo study

Monte Carlo methods in the presence and absence of an external magnetic field were used to investigate the thermodynamic and magnetic properties of the mixed spins (3/2, 3) Ising ferrimagnets in a 2D triangular lattice consisting of sublattices A, B, and C. Two types of mixing were considered: S→=(SA,SB,SC)=(3/2,3,3) (Model I) and S→=(SA,SB,SC)=(3/2,3,3/2) (Model II). In contrast to bipartite lattices, the antiferromagnetic coupling between spin-3/2 and spin-3 in the triangular lattice leads to geometric frustrations that impact magnetic properties. Determination of ground state phase diagrams, combined with verification of whether or not there was magnetic hysteresis when crossing each transition line, revealed first- and second-order phase transition lines, as well as multicritical points. The temperature investigation in the absence of an external magnetic field revealed rich magnetic properties such as 1st- and 2nd-order phase transitions, N- and L-type compensation points, tricritical points, and critical endpoints, as well as M-, P-, Q-, R- and S-type total magnetization behaviours. The effect of the crystal field on finite-temperature phase diagrams and compensation behaviour was also carried out. As a result, the critical temperatures of Model II become constant when the crystal field is sufficiently strong. In contrast, several critical values of the crystal field for which the critical temperature is zero were identified for Model I. In the presence of a magnetic field, hysteresis behaviour and associated magnetic properties such as coercivity and magnetic remanence were investigated. The effect of crystal field and temperature was explored. Hysteresis of one to four loops were found at low temperatures when the crystal field varied. Finally, as the temperature rises, the hysteresis loops' area decreases to zero at high temperatures.

Tricriticality in 4D U(1) lattice gauge theory

The 4D compact U(1) gauge theory has a well-established phase transition between a confining and a Coulomb phase. In this paper, we revisit this model using state-of-the-art Monte Carlo simulations on anisotropic lattices. We map out the coupling-temperature phase diagram, and determine the location of the tricritical point, T/K0≃0.19, below which the first-order transition is observed. We find the critical exponents of the high-temperature second-order transition to be compatible with those of the 3-dimensional O(2) model. Our results at higher temperatures can be compared with literature results and are consistent with them. Surprisingly, below T/K0≃0.05 we find strong indications of a second tricritical point where the first-order transition becomes continuous. These results suggest an unexpected second-order phase transition extending down to zero temperature, contrary to the prevailing consensus. If confirmed, these findings reopen the question of the detailed characterization of the transition including a suitable field theory description. Published by the American Physical Society 2024

Metastable states in the Ising model with Glauber-Kawasaki competing dynamics.

Metastable states are identified in the Ising model with competition between the Glauber and Kawasaki dynamics. The model of interaction between magnetic moments was implemented on a network where the degree distribution follows a power law of the form P(k)∼k^{-α}. The evolution toward the stationary state occurred through the competition between two dynamics, driving the system out of equilibrium. In this competition, with probability q, the system was simulated in contact with a heat bath at temperature T by the Glauber dynamics, while with probability 1-q, the system experienced an external energy influx governed by the Kawasaki dynamics. The phase diagrams of T as a function of q were obtained, which are dependent on the initial state of the system, and exhibit first- and second-order phase transitions. In all diagrams, for intermediate values of T, the phenomenon of self-organization between the ordered phases was observed. In the regions of second-order phase transitions, we obtained the critical exponents of the order parameter β, susceptibility γ, and correlation length ν. Furthermore, in the regions of first-order phase transitions, we have demonstrated the instability due to transitions between ordered phases through hysteresislike curves of the order parameter, in addition to the existence of absorbing states. We also estimated the value of tricritical points when the discontinuity in the order parameter in the phase transitions was no longer observed.

Avoided Quantum Tricritical Point and Emergence of a Canted Magnetic Phase in LaCr_{1-x}Fe_{x}Sb_{3}.

New phases or new phenomena are often observed near-zero temperature phase transitions. These new effects represent nature's way of avoiding quantum critical phase transitions. Here, we look at the quantum tricritical point (QTCP), the special case where two transitions are driven to zero temperature at the same time. Unlike the case of quantum critical points, the avoidance of quantum tricritical points has yet to be demonstrated. Using chemical substitution and a magnetic field, we drive LaCrSb_{3} toward a quantum tricritical point. For the first time near a QTCP, we observe the emergence of a new magnetic phase and the avoidance of the QTCP via a first order phase transition.

Entropy-induced phase transitions in a hidden Potts model.

A hidden state in which a spin does not interact with any other spin contributes to the entropy of an interacting spin system. We explore the q-state Potts model with extra r hidden states using the Ginzburg-Landau formalism in the mean-field limit. We analytically demonstrate that when 1<q≤2, the model exhibits a rich phase diagram comprising a variety of phase transitions such as continuous, discontinuous, two types of successive, and hybrid transitions; moreover, several characteristics such as critical point, critical endpoint, and tricritical point are identified. The critical line and critical endline merge in a singular form at the tricritical point. That supercritical behavior emerging at the tricritical point is, to the best our knowledge, novel. We microscopically investigate the origin of the discontinuous transition; it is induced by the competition between the interaction and entropy of the system in the Ising limit, whereas by the bistability of the hidden spin states in the percolation limit. Finally, we discuss the similarity and difference of the phase diagram generated in two types of Ising spins model.

The frustrated bilayer Ising model: A cluster mean-field approach

We investigate the Ising model on the bilayer square lattice with antiferromagnetic interactions between first-(J1) and second-neighbors (J2) inside each layer and a perpendicular antiferromagnetic interaction (Jp) between layers. The roles of frustration and interlayer interactions on the thermal phase transitions are described within a variational cluster mean-field (CMF) approach. For J2/J1<1/2, the model exhibits a Néel antiferromagnetic (AF) ground state and, for J2/J1>1/2, a stripe antiferromagnetic (SAF) ground state takes place. In the absence of interlayer interactions, a tricritical point is found in the phase boundary between SAF and paramagnetic (PM) phases. Our CMF calculations show that the ordering temperature of both AF and SAF phases is enhanced by the interlayer couplings. We also show that, at different levels of frustration, in the strong-interlayer-coupling limit, the ordering temperature is twice the one in the absence of interlayer interactions. At the weak-interlayer-coupling limit, a linear dependence of the ordering temperature with the interlayer interaction is observed, which indicates a shift exponent ϕ=1. Our investigation revealed that the model exhibits tricriticality at all strengths of the interlayer interactions, but the coupling coordinate of the tricritical point (J2/J1)t exhibits a minimum at a finite strength of Jp/J1. However, in the strong interlayer coupling limit, the coupling coordinate of the tricritical point is the same as in the decoupled (Jp=0) limit. Therefore, our CMF study reveals a persistent tricriticality in the frustrated bilayer Ising model.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions.

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

Field-induced effects and ferroelectric critical endpoint in (K0.95Li0.05)(Nb1–x Ta x )O3 single crystals

Dielectric permittivities under dc biasing fields in the temperature range between –169 °C and 75 °C have been investigated in (K0.95Li0.05)(Nb1–x Ta x )O3 (KLNT–x, x = 71% and 74%). Field-induced ferroelectric phase transitions in KLNT–x have been clarified in the dc field applied along the [001] c direction (in the cubic coordinate). The ferroelectric critical endpoints in KLNT–71% and KLNT–74% have been determined to be 43.5 °C, 3.0 kV cm−1, and 30.3 °C, 2.0 kV cm−1, respectively. The tricritical point at which the first-order phase transition changes to the second-order phase transition has been estimated at 10.4 °C and x = 77.4% in the temperature–concentration phase diagram. The field-induced phase transitions and dielectric tunabilities have been discussed on the basis of the Landau-type free energy density.

Perturbation-tuned triple spiral metamagnetism and tricritical point in kagome metal ErMn6Sn6

Kagome materials are of topical interest for their diverse quantum properties linked with correlated magnetism and topology. Here, we report anomalous hydrostatic pressure (p) effect on ErMn6Sn6 through isobaric and isothermal-isobaric magnetization measurements. Magnetic field (H) suppresses antiferromagnetic TN while simultaneously enhancing the ferrimagnetic TC by exhibiting dual metamagnetic transitions, arising from the triple-spiral-nature of Er and Mn spins. Counter-intuitively, pressure enhances both TC and TN with a growth rate of 74.4 K GPa−1 and 14.4 K GPa−1 respectively. Pressure unifies the dual metamagnetic transitions as illustrated through p-H phase diagrams at 140 and 200 K. Temperature-field-pressure (T-H, T-p) phase diagrams illustrate distinct field- and pressure-induced critical points at (Tcr = 246 K, Hcr = 23.3 kOe) and (Tcr = 435.8 K, pcr = 4.74 GPa) respectively. An unusual increase of magnetic entropy by pressure around Tcr and a putative pressure-induced tricritical point pave a unique way of tuning the magnetic properties of kagome magnets through simultaneous application of H and p.

Existence of a tricritical point for the Blume–Capel model on ℤd

Existence of a tricritical point for the Blume–Capel model on ℤd

The impact of segment dilution on the magnetic and hysteretic properties of ferrimagnetic (1/2-1) segmented Ising nanowire

This study explores the presence of diverse phase diagrams and hysteresis characteristics, as well as their dependencies on segment dilution, in an Ising-type core/shell segmented nanostructure. The magnetic and hysteretic behavior of the nanostructure was carefully investigated by employing the effective-field theory and its respective diluted parameters. The phase diagrams reveal characteristic phenomena that are influenced by the dilution parameters. Specifically, this study examined the variations in phase transitions and tricritical points by altering the dilution and physical parameters of the segments. The investigation also encompasses an examination of the hysteresis characteristics, including the hysteresis loop, coercivity, and remanence, in relation to the segment dilution dependence of the segmented nanowire. It was discovered that as the temperature rises, the hysteresis loop areas diminish. However, intriguingly, at specific dilution and crystal area values, the hysteresis loop areas exhibit an augmentation.

Quantum tricriticality in a generalized quantum Rabi system

Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a non-trivial parameter to adjust the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analysis on quantum fluctuations and the average photon number, universal critical exponents differentiate the QTCP from the second-order critical point. Our results indicate that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.

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.