Tricritical Point Research Articles

Quantum Simulation of the Tricritical Ising Model in Tunable Josephson Junction Ladders.

Modern hybrid superconductor-semiconductor Josephson junction arrays are a promising platform for analog quantum simulations. Their controllable and nonsinusoidal energy-phase relation opens the path to implement nontrivial interactions and study the emergence of exotic quantum phase transitions. Here, we propose the analysis of an array of hybrid Josephson junctions defining a two-leg ladder geometry for the quantum simulation of the tricritical Ising phase transition. This transition provides the paradigmatic example of minimal conformal models beyond Ising criticality and its excitations are intimately related to Fibonacci non-Abelian anyons and topological order in two dimensions. We study this superconducting system and its thermodynamic phases based on bosonization and matrix-product-state techniques. Its effective continuous description in terms of a three-frequency sine-Gordon quantum field theory suggests the presence of the targeted tricritical point and the numerical simulations confirm this picture. Our results indicate which experimental observables can be adopted in realistic devices to probe the physics and the phase transitions of the model. Additionally, our proposal provides a useful one-dimensional building block to design exotic topological order in two-dimensional scalable Josephson junction arrays.

Exploring the nematic to twist-bend nematic phase transition: calorimetric and optical measurements

ABSTRACT We investigate the nematic (N) to twist-bend nematic (NTB) phase transition in binary mixtures of a symmetric liquid crystal dimer (CB7CB) and a calamitic bi-phenyl mesogen (7OCB). As the molar concentration of 7OCB increases, both the Iso–N and N–NTB transition temperatures decrease gradually, consequently, the width of the nematic phase above the NTB phase can suitably be varied from ~12 K to 46 K. Notably, as the nematic range expands, there is a remarkable reduction in transitional entropy, eventually approaching negligible or zero values. Additionally, the heat capacity peak and the phase shift disappear when transitional entropy reaches zero. This behaviour diverges from typical N–SmA and N–SmC phase transitions, where transitional entropy decreases near the tricritical point but the heat capacity peak persists. Our findings indicate a finite positive δ(∆n) across all concentrations at the N–NTB phase transition, suggesting a gradually weakening first-order nature. This contrasts with theoretical predictions of a second-order N–NTB phase transition, as our experimental data consistently supports a first-order nature. The self-consistent mean-field Landau Model successfully validates our experimental data, establishing the universal first-order nature of the N–NTB phase transition, with experimental entropy values in good agreement with theoretical prediction.

A Spectral Investigation of Criticality and Crossover Effects in Two and Three Dimensions: Short Timescales with Small Systems in Minute Random Matrices.

Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume-Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior.

Magnetic behaviors of diatomic molecules with mixed spin-1 and spin-1/2 on the Bethe lattice

It is considered that each Bethe lattice (BL) site is inhabited by a diatomic molecule made up of either two spin-1/2 or two spin-1 atoms, respectively. Then, each diatomic molecule is thought to interact with others via its atoms in terms of numerous bilinear interaction parameters, such as the interaction of atoms within each molecule and the interaction of atoms between molecules. The thermal fluctuations of magnetizations for the diatomic molecule are examined by incorporating a crystal field for the spin-1 atoms and mapping their magnetic phase diagrams on the BL with coordination number q=3 using exact recursion relations (ERR). The effects of the external magnetic field are also taken into account while analyzing the thermal fluctuations in magnetizations. For various antiferromagnetic (AFM) and ferromagnetic (FM) interaction setups, the model always presents second- and first-order phase lines merging at a tricritical point (TCP). The acquired results are compared to those of a BL, in which each site is associated with only one atom.

Exact Matrix Product States at the Quantum Lifshitz Tricritical Point in a Spin-1/2 Zigzag-Chain Antiferromagnet with Anisotropic Γ Term.

Quantum anisotropic exchange interactions in magnets can induce competitions between phases in a different manner from those typically driven by geometrically frustrated interactions. We study a one-dimensional spin-1/2 zigzag chain with such an interaction, Γ term, in conjunction with the Heisenberg interactions. We find a ground state phase diagram featuring a multicritical point where five phases converge: a uniform ferromagnet, two antiferromagnets, Tomonaga-Luttinger liquid, and a dimer-singlet coexisting with nematic order. This multicritical point is simultaneously quantum tricritical and Lifshitz, and most remarkably, it hosts multidegenerate ground state wave functions with the degeneracy increasing in squares of system size. The exact ground states are obtained in the matrix product form opening wide applications to frustration-free models.

Thermodynamics of charged black holes in Maxwell-dilaton-massive gravity* *Supported by the National Key Research and Development Program of China (2020YFC2201400). D. C. Zou is supported by the National Natural Science Foundation of China (12365009), and the Natural Science Foundation of Jiangxi Province, China (20232BAB201039)

Considering the nonminimal coupling of the dilaton field to the massive graviton field in Maxwell-dilaton-massive gravity, we obtain a class of analytical solutions of charged black holes, which are neither asymptotically flat nor (A)dS. The calculated thermodynamic quantities, such as mass, temperature, and entropy, verify the validity of the first law of black hole thermodynamics. Moreover, we further investigate the critical behaviors of these black holes in the grand canonical and canonical ensembles and find a novel critical phenomenon never before observed, known as the "reverse" reentrant phase transition with a tricritical point. It implies that the system undergoes a novel "SBH-LBH-SBH" phase transition process and is the reverse of the "LBH-SBH-LBH" process observed in reentrant phase transitions.

Blume-Capel model analysis with a microcanonical population annealing method.

We present a modification of the Rose-Machta algorithm [N. Rose and J. Machta, Phys. Rev. E 100, 063304 (2019)2470-004510.1103/PhysRevE.100.063304] and estimate the density of states for a two-dimensional Blume-Capel model, simulating 10^{5} replicas in parallel for each set of parameters. We perform a finite-size analysis of the specific heat and Binder cumulant, determine the critical temperature along the critical line, and evaluate the critical exponents. The obtained results are in good agreement with those previously obtained using various methods-Markov chain Monte Carlo simulation, Wang-Landau simulation, transfer matrix, and series expansion. The simulation results clearly illustrate the typical behavior of specific heat along the critical lines and through the tricritical point.

Binder Parameter in a Generalized Two-dimensional XY Model

We performed Monte Carlo simulation for a two-dimensional generalized XY model and calculated the magnetic and nematic Binder parameters. The phase diagram is re-examined based on these Binder parameters, demonstrating their power in studying generalized XY models. The Binder parameter has distinctive behaviors, resulting in different types of phase transition. More importantly, the magnetic Binder parameter gives more insights into the tricritical region where the Kosterlitz-Thouless, Ising, and 1/2 Kosterlitz-Thouless (KT) transition lines meet. It shows signatures for the intermediate region starting from the tricritical point, where the transition line is neither the same physics as the Ising transition below nor the KT transition far above the tricritical point.

Kinetic phase phenomena of model with the chemical formula [formula omitted] on honeycomb lattice

We investigate the ferromagnetic–ferrimagnetic ternary alloy model with the chemical formula ABpC1−p with mean-field theory based on Glauber-type stochastic dynamics, namely dynamic mean-field theory, on a honeycomb lattice consisting of spins SiA=1/2, SjB=3/2 and SjC=5/2. The model includes a selective site disorder, meaning that SiA can randomly have SjC as its nearest neighbor or SjB with probability (1−p). The mean-field dynamic equations were obtained and numerically solved. To identify the type of dynamic phase transitions (first- or second-order), the thermal behavior of dynamic magnetizations was examined. For specified values of the crystal field parameter, exchange interaction parameter, and concentration ratio, the phase diagrams are calculated in the (d−T) and (T−h) planes. The system's fundamental and mixed-phase areas were identified. The system displayed A,TP,QP,Z special points and dynamic tricritical points. It was found that the content of the ternary alloy continuously affected the critical temperature in our dynamic system. Reliable agreements are observed when our findings are compared to those in the literature.

Light Roberge-Weiss tricritical endpoint at imaginary isospin and baryon chemical potential

Imaginary chemical potentials serve as a useful tool to constrain the QCD phase diagram and to gain insight into the thermodynamics of strongly interacting matter. In this study, we report on the first determination of the phase diagram for arbitrary imaginary baryon and isospin chemical potentials at high temperature using one-loop perturbation theory, revealing a nontrivial structure of Roberge-Weiss (RW) phase transitions in this plane. Subsequently, this system is simulated numerically with Nf=2 unimproved staggered quarks on Nτ=4 lattices at a range of temperatures at one of the RW phase transitions. We establish a lower bound for the light quark mass, where the first-order transition line terminates in a tricritical point. It is found that this tricritical mass is increased as compared to the case of purely baryonic imaginary chemical potentials, indicating that our setup is more advantageous for identifying critical behavior toward the chiral limit. Finally, the dynamics of local Polyakov loop clusters is also studied in conjunction with the RW phase transition. Published by the American Physical Society 2024

Revealing magnetic and physical properties of TbFe4.4Al7.6: experiment and theory

We report on the magnetic, electrical transport, caloric and electronic structure properties of TbFe4.4Al7.6 polycrystalline alloy using experiment and theory. The alloy crystallizes in tetragonal structure with I4/mmm space group with lattice parameters a = b = 8.7234(5) Å and c = 5.0387(6) Å. It is ferrimagnetic with a compensation temperature of Tcmp∼ 151 K, Curie–Weiss temperature θCW∼ 172.11 K and an effective magnetic moment μeff = (2.37±0.07) μB /f.u with Z = 2. At low temperatures, kinetic arrest-like first-order phase transition is realized through the thermal hysteresis between field-cooled cooling and field-cooled warming curves of M(T) and virgin curves of M(H) and ρ(H) which are outside the hysteresis loops with metamagnetic transition. The high magnetic field suppression of multiple transitions and reduced coercive field Hcoer and remnant magnetization Mrem with increasing temperature are reported. Hcoer and Mrem cease to exist above the compensation temperature Tcmp . A correlation between the isothermal magnetization and resistivity is discussed. Specific heat C(T) analysis reveals a Sommerfeld parameter of γ = 0.098 J⋅mol−1⋅K−2 and a Debye temperature of θD∼351.2 K. The sample is metallic as inferred from the ρ(T) behavior and Sommerfeld parameter. The magnetoresistance of the alloy is low and negative which indicates the suppression of weak spin-fluctuations. This alloy avoids the tricritical point despite first-to-second order phase transition. The electronic and magnetic structure calculations, by making use of full potential linearized augmented plane wave method, suggest metallic ferrimagnetic ground state of TbFe4.4Al7.6 with Tb atoms contributing ferromagnetically (5.87 μB ) and Fe atoms with antiferromagnetic contribution (2.67 μB ), in close agreement with the experimental observation.

Optimizing the random search of a finite-lived target by a Lévy flight.

In many random search processes of interest in chemistry, biology, or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results on a minimal model system, a one-dimensional searcher performing a discrete time random walk, or Lévy flight. In contrast with the case of a permanent target, the capture probability and the conditional mean first passage time can be optimized. The optimal Lévy index takes a nontrivial value, even in the long lifetime limit, and exhibits an abrupt transition as the initial distance to the target is varied. Depending on the target lifetime, this transition is discontinuous or continuous, separated by a nonconventional tricritical point. These results pave the way to the optimization of search processes under time constraints.

Critical and tricritical singularities from small-scale Monte Carlo simulations: the Blume–Capel model in two dimensions

We show that accurate insights into the critical properties of the Blume–Capel model at two dimensions can be deduced from Monte Carlo simulations, even for small system sizes, when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins. We also show that the zeros are very sensitive to subtle crossover effects.

Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom

We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of the model and the associated closed set of equations of state involving four order parameters, proving the integrability and exact solvability of the model. The equations of state are specified via a suitable representation of the orientational order parameters, which imply two-order parameter reductions in the absence of external fields. A detailed exact analysis of the equations of state reveal a rich phase diagram where isotropic versus uniaxial versus biaxial phase transitions are explicitly described, including the existence of triple and tricritical points. Results on the discrete models are qualitatively consistent with their continuum analogue. This observation suggests that, in more general settings, discrete models may be used to capture and describe phenomena that also occur in the continuum for which exact equations of state in closed form are not available.

Bicontinuous microemulsion in binary blends of complementary diblock copolymers.

The phase behavior of binary blends of AB diblock copolymers of compositions f and 1 - f is examined using field-theoretic simulations. Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (i.e., f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f = 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz point should be destroyed by fluctuations. Consistent with this, it is found to transform into a tricritical point. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz point disorders into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate. Our alternative system for creating BμE is free of this macrophase separation.

Magnetic behavior of a diatomic molecule with spin-1 on the Bethe lattice

Thermal fluctuations in magnetizations and magnetic phase diagrams of a diatomic molecule are investigated on the Bethe lattice (BL) with coordination number q=3 by using the exact recursion relations (ERR). Each molecule is assumed to interact with others via its atoms in terms of various bilinear interaction parameters. They involve the interaction of atoms within each molecule as well as the interaction of atoms between the molecules. Each site is also considered to have an active crystal field. Following the determination of the average magnetization of the molecule and its atoms in the central molecule of the BL in terms of ERR, their thermal fluctuations and potential phase diagrams are thoroughly analyzed. Numerous phase regions, ordered (O), i.e., ferromagnetic (FM) or antiferromagnetic (AFM), paramagnetic (P), and random (R), are discovered. The phase boundaries between these phases are obtained in terms of first- and second-order and random phase transition lines. Therefore, various critical phenomena, including tricritical point (TCP), bicritical point (BCP), critical end point (CEP) and reentrant behavior (RB), are observed.

Non-equilibrium magnetic properties of a mixed spin (1/2, 1) Ising graphene nanoisland.

Based on Glauber-type stochastic dynamics intertwined with mean field theory, we have investigated a graphene nanoisland's out-of-equilibrium magnetic and thermomagnetic behaviors with a mixed ferrimagnetic spin (1/2, 1) configuration in the presence of an oscillating magnetic field. The influence of the oscillating external magnetic field, single-ion anisotropy and temperature on the dynamic magnetic properties (dynamic phase transitions, hysteresis loop areas, correlations, and phase diagrams) of the system is studied in detail. The results illustrate that single ion anisotropy and the magnetic field play important roles in the system's dynamic order parameters, phase transitions and phase diagrams. Dynamic phase diagrams display some dynamic special points such as dynamic tricritical points, quadruple points and some sort of reentrant phenomena, which strongly depend on interaction parameters. Our predicted results may provide a reference for future experimental and theoretical studies of the nanostructures.

Optical and calorimetric studies near the smectic-A to smectic-C tricritical point

Detailed heat capacity and birefringence measurements have been performed to investigate the transitional behavior near the orthogonal smectic-A to tilted smectic-C (Sm-A–Sm-C) phase transition on several liquid crystalline mixtures comprising of a rod-like mesogen and a hockey stick-shaped compound having substitution of methyl group in the lateral position. Both probing methods were found to be rather successful in assessing the phase transitional behavior with reasonably good accuracy. The data shows a divergent pretransitional excess above and below the transition temperature. Analysis of the data have been performed in detail with the renormalization-group expression with correction-to-scaling terms. The extracted effective critical exponents were observed in between the tricritical and 3D-XY limit. Detailed investigations carried out in this work reveal the dependence of the Sm-A–Sm-C phase transition on the width of the Sm-A phase and the existence of a broad tricritical range.

Phase transitions and slow spin dynamics of slightly inverted A-site spinel CoAl2−x Ga x O4

We report the properties of an A-site spinel magnet, CoAl2−x Ga x O4, and analyze its anomalous, low-temperature magnetic behavior, which is derived from inherent, magnetically frustrated interactions. Rietveld analysis of the x-ray diffraction profile for CoAl2−x Ga x O4 revealed that the metallic ions were randomly distributed in the tetrahedral (A-) and octahedral (B-) sites in the cubic spinel structure. The inversion parameter η could be controlled by varying the gallium (Ga) composition in the range 0.055 ⩽ η ⩽ 0.664. The composition-induced Néel-to-spin-glass (NSG) transition occurred between 0.05 ⩽ η ⩽ 0.08 and was verified by measurements of DC-AC susceptibilities χ and thermoremanent magnetization (TRM) below the Néel transition temperature T N. The relaxation rate and derivative with respect to temperature of TRM increased at both T N and the spin glass (SG) transition temperature T SG. The TRM decayed rapidly above and below these transitions. TRM was highly sensitive to macroscopic magnetic transitions that occurred in both the Néel and SG phases of CoAl2−x Ga x O4. In the vicinity of the NSG boundary, there was a maximum of the TRM relaxation rate at T max < T N. With increasing inversion η(x), the anomaly at T max merged with that of the Néel transition at a tricritical point (η tc, T tc) = (0.08, 4.0 K), where the paramagnetic, Néel, and SG states met. We successfully extracted the relaxation time τ and other characteristic parameters from the TRM isothermal temporal evolution based on the Weron function derived for a purely stochastic process. To distinguish the magnetic states, we compared our results with previously studied inversion-free A-site spinel, CoRh2O4, and CoGa2O4 cluster glass. We generated an inversion-temperature phase diagram based on the comprehensive measurements of DC and AC susceptibilities, TRM, and specific heat in the range 0.055 ⩽ η ⩽ 0.664 for CoAl2−x Ga x O4. Based on this phase diagram, we speculate that a NSG quantum critical phase transition occurred at η = 0.050(6). Our findings are consistent with suppression of the long-range order antiferromagnetic state in CoAl2O4 revealed through neutron diffraction studies, even at T << T N.

Estimating phase transition of perturbed Heisenberg quantum chain in mixtures of ground and first excited states

We show that the nearest neighbour entanglement in a mixture of ground and first excited states—a subjacent state—of the Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small finite probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to separate introductions of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point in the former case. The anisotropic chain has a richer phase diagram which is also clearly visible by using the same order parameter.