Bicritical Point Research Articles

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.

Deconfined quantum criticality of nodal d -wave superconductivity, Néel order, and charge order on the square lattice at half-filling

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the π-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background π-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal d-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by (2+1)-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional d-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases. Published by the American Physical Society 2024

Emergent tetragonality in a fundamentally orthorhombic material.

Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material remain invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. Less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. We find signatures of an emergent tetragonal symmetry close to a charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe3, for which the two distinct CDW phase transitions are tuned via anisotropic strain. We first establish that tension along the a axis favors an abrupt rotation of the CDW wave vector from the c to a axis and infer the presence of a bicritical point where the two continuous phase transitions meet. We then observe a divergence of the nematic elastoresistivity approaching this putative bicritical point, indicating an emergent tetragonality in the critical behavior.

Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement

Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX−YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan–Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin–spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.

Quantum reaction-limited reaction–diffusion dynamics of noninteracting Bose gases

We investigate quantum reaction–diffusion (RD) systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ( A+A→∅ ) and coagulation ( A+A→A ) of particles at distance d. We consider the reaction-limited regime, where dissipative reactions take place at a rate that is small compared to that of coherent hopping. In classical RD systems, this regime is correctly captured by the mean-field approximation. In quantum RD systems, for noninteracting fermionic systems, the reaction-limited regime recently attracted considerable attention because it has been shown to give universal power law decay beyond mean field for the density of particles as a function of time. Here, we address the question whether such universal behavior is present also in the case of the noninteracting Bose gas. We show that beyond mean-field density decay for bosons is possible only for reactions that allow for destructive interference of different decay channels. Furthermore, we study an absorbing-state phase transition induced by the competition between branching A→A+A , decay A→∅ and coagulation A+A→A . We find a stationary phase-diagram, where a first and a second-order transition line meet at a bicritical point which is described by tricritical directed percolation. These results show that quantum statistics significantly impact on both the stationary and the dynamical universal behavior of quantum RD systems.

The spin-5/2 Blume–Capel model by mean-field approach and renormalization group theory

The spin-5/2 Blume–Capel model was studied using the mean-field approximation and the Migdal–Kadanoff renormalization group method for two- and three-dimensional systems. We determined the phase diagrams in the (crystal field, temperature) plane where the system exhibited first- and second-order phase transitions as well as isolated critical, bicritical and triple points. In order to show first-order transitions at low temperature, we presented the total magnetization per site and the derivative of the free energy as a function of the crystal field. Moreover, the critical exponents of the system were calculated by linearizing the renormalization transformation at the vicinity of the second-order fixed points.

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.

Quantum bicritical point and phase separation in a frustrated Heisenberg ladder

Quantum bicritical point and phase separation in a frustrated Heisenberg ladder

Stochastic analysis of chemical reactions in multi-component interacting systems at criticality

We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schlögl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in the reaction kinetics, with these critical lines coalescing at a bicritical point in the macroscopic limit. We construct a stochastic master equation for the reaction processes to account for the presence of mutual particle interactions in a thermodynamically consistent manner by imposing a generalized detailed balance condition, which leads to exponential corrections for the transition rates. In a non-spatially extended (zero-dimensional) setting, we treat the interactions in a mean-field approximation, and introduce a minimal model that encodes the physical behavior of the bicritical point and permits the exact evaluation of the anomalous scaling for the particle number fluctuations in the thermodynamic limit. We obtain that the system size scaling exponent for the particle number variance changes from at the standard non-interacting bifurcation to at the interacting bicritical point. The methodology developed here provides a generic route for the quantitative analysis of fluctuation effects in chemical reactions occurring in multi-component interacting systems.

Effective exponents near bicritical points

Effective exponents near bicritical points

My encounters with Alex Müller and the perovskites

This paper is dedicated to the memory of Professor K. Alex Müller. After describing our personal and scientific encounters since 1974, I concentrate on the many puzzles which appeared in our discussions and collaborations, involving the interplay between theory and experiments on the critical behavior of cubic perovskites which undergo (second or first) order transitions to a lower symmetry phases (trigonal or tetragonal). The conclusion, reached only very recently, is that (although beginning with the same cubic symmetry) the two types of transitions belong to two distinct universality classes: under [100] stress, the cubic to trigonal transition exhibits a tetracritical phase diagram, with ‘cubic’ exponents, while the cubic to tetragonal transition exhibit an ‘intermediate’ bicritical phase diagram, but asymptotically the bicritical point turns into a triple point, with three first order lines. To test these conclusions, it is suggested to measure the effective critical exponents as the temperature approaches criticality.

Effects of finite depth and surface tension on the linear and weakly non-linear stability of Faraday waves in Hele-Shaw cell

A linear and a non-linear analysis are carried out for the instability of the free surface of a liquid layer contained in a Hele-Shaw cell subjected to periodic vertical oscillation. The linear stability analysis shows that for certain ranges of the oscillation frequency, the depth of the liquid layer and the surface tension can have a substantial effect on the selection of the wavenumbers and on the critical forcing amplitude. This results in a new dispersion relation, relating the critical wavenumber and the frequency of oscillation, which is in excellent agreement with recent experimental results by Li et al (2018 Phys. Fluids 30 102103). On the other hand, for low frequencies, the thresholds can be either harmonic or subharmonic with the existence of a series of bicritical points where these two types of thresholds can coexist. Weakly nonlinear analysis is performed in the vicinity of the first subharmonic resonance that occurs in the high frequency limit. Thus, using the multiscale technique, for low dissipation and forcing, we derive a free surface amplitude equation, involving a new nonlinear term coefficient, χ, that includes finite depth and surface tension. For infinite depth, Rajchenbach et al (2011 Phys. Rev. Lett. 107 024502), and Li et al (2019 J. Fluid Mech. 871 694–716) showed that hysteresis can only occur if the response frequency is lower than the natural frequency. However in the present work, it turns out that the coefficient χ can be either positive or negative depending on the depth and surface tension of the fluid. Thus, if χ is positive, hysteresis is found when the response frequency is greater than the natural frequency. Furthermore, the infinite depth approximation, where the short wavelengths dominate, is valid when the depth and wavenumber satisfy kh > 5, whereas for kh < 5, where long wavelengths dominate, the finite depth should be considered.

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume–Capel model and the repulsive Blume–Emery–Griffiths model, the tricritical point splits into a critical end point and a bicritical end point with an increase in disorder and repulsive coupling strength respectively. In order to make a distinction between these two multicritical points, we investigate and contrast the behaviour of the first order phase boundary and the co-existence diameter around them.

Negative/positive electrocaloric effect in antiferroelectric squaric acid

Using the previously developed model, we study the electrocaloric effect (ECE) in antiferroelectric crystals of squaric acid, where the low-temperature polarization reorientation by the external electric field has been earlier predicted to be a two-stage process with the intermediate ferrielectric phase. The T-E landscape of the model entropy is explored. The ECE, characterized by the electric Grüneisen parameter, is found to be negative in the antiferroelectric phase. In the ferrielectric phase, it is positive at low fields but becomes slightly negative below the transition to the ferroelectric phase. In the ferroelectric phase, the ECE is positive at all temperatures and fields. The negative EC temperature shift ΔT of the largest magnitude is predicted to be around −2.7 K at 200 kV/cm. The supercritical behavior of the Grüneisen parameter in the crossover region between two bicritical end points is studied.

Distinguishing dxz+idyz and dx2−y2 pairing in Sr2RuO4 by high magnetic field H−T phase diagrams

Employing a realistic tight-binding model describing the Fermi surface in the normal state of $Sr_2RuO_4$ we map out magnetic field versus temperature phase diagrams for $d_{x^2-y^2} (B_{1g})$ and $d_{xz}+id_{yz} (E_g)$ pairing types. Both produce (i) a similar Knight shift suppression of $\sim\!80\%$ and (ii) a bicritical point at $T=0.88$K separating low field second order phase transitions from high field Pauli limiting first order transitions. We find, however, strikingly different phase behaviour within the high field Pauli limiting region. For $d_{x^2-y^2}$ pairing symmetry an additional lower critical line of first order transitions is found (terminating in a critical point at $T=0.09-0.22$K depending on the choice of Hubbard U parameters) while for $d_{xz}+id_{yz}$ no such additional high field phase transitions are found for any choice of Hubbard U. In conjunction with our earlier finding [{\it Physical Review B} {\bf 102} (23), 235203] for $p$-wave helical pairing of a still different high field phase structure (a lower critical field line meeting the upper critical field line exactly at the bicritical point), we suggest high field Pauli limiting phase structure as a possible route to distinguish pairing symmetries in this material.

The spin-1 XYZ model with Dzyaloshinskii–Moriya interaction

The spin-1 XYZ model is studied in terms of a mean-field (MF) approach by introducing the spin operators on honeycomb lattice. The considered Hamiltonian consists of a bilinear exchange interaction parameter (Jz) and a single-ion anisotropy (Dz) only along the z-axis, in addition to the Dzyaloshinskii–Moriya interaction (Δm). The external magnetic field is introduced in all three dimensions and their behaviors are examined on the components of magnetization. Then the thermal behaviors of magnetizaitons are investigated in detail to obtain the phase diagrams on the (Dz/J,kT/J) and (Δm/J,kT/J) planes when the external magnetic field components are turned off. It is found that the model gives both first- and second-order phase transitions in addition to a few types critical points including the tricritical and bicritical points.

Phase Transitions in the Blume–Capel Model with Trimodal and Gaussian Random Fields

We study the effect of different symmetric random field distributions: trimodal and Gaussian on the phase diagram of the infinite range Blume–Capel model. For the trimodal random field, the model has a very rich phase diagram. We find three new ordered phases, multicritical points like tricritical point (TCP), bicritical end point (BEP), critical end point (CEP) along with some multi-phase coexistence points. We also find re-entrance at low temperatures for some values of the parameters. On the other hand for the Gaussian distribution the phase diagram consists of a continuous line of transition followed by a first order transition line, meeting at a TCP. The TCP vanishes for higher strength of the random field. In contrast to the trimodal case, in Gaussian case no new phase emerges.

Bi- and tetracritical phase diagrams in three dimensions

The critical behavior of many physical systems involves two competing n1- and n2-component order-parameters, S1 and S2, respectively, with n = n1 + n2. Varying an external control parameter g, one encounters ordering of S1 below a critical (second-order) line for g &amp;lt; 0 and of S2 below another critical line for g &amp;gt; 0. These two ordered phases are separated by a first-order line, which meets the above critical lines at a bicritical point, or by an intermediate (mixed) phase, bounded by two critical lines, which meet the above critical lines at a tetracritical point. For n = 1 + 2 = 3, the critical behavior around the (bi- or tetra-) multicritical point either belongs to the universality class of a non-rotationally invariant (cubic or biconical) fixed point, or it has a fluctuation driven first-order transition. These asymptotic behaviors arise only very close to the transitions. We present accurate renormalization-group flow trajectories yielding the effective crossover exponents near multicriticality.

Pressure-induced multicriticality and electronic instability in the quasi-kagome ferromagnet URhSn

We report an unconventional class of pressure-induced quantum phase transitions, possessing two bicritical points at 6.25 GPa in URhSn. This unique transformation accompanies a Fermi surface reconstruction, demarcating competing ordered phases suitably described with a localized and itinerant description of the magnetic $5f$ electrons. Ferromagnetic fluctuations over a wide range of temperatures and pressures in the pressure-induced low temperature phase are evidenced by a robust ${T}^{5/3}$ temperature dependence of resistivity up to 11 GPa, which is a characteristic of an elusive marginal Fermi-liquid state.

Noether-Wald charges in six-dimensional Critical Gravity

It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory — originally found by Lu, Pang and Pope (LPP) — can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.