Bicritical Point Research Articles

Antiferromagnetism and superconductivity transitions with SO (5) symmetry

Using Monte Carlo simulation we have computed the phase diagram of a superspin model of the SO(5) symmetry between antiferromagnetism (AF) and d-wave superconductivity (SC). A bicritical point is observed at a finite temperature where the second-order AF and SC transition lines merge tangentially into a first-order line in the temperature vs. doping rate phase diagram. In the regime of the doping rate where the SC is achieved at low temperatures, maximal AF correlation length is observed at a temperature above the SC transition point T c when AF coupling is much stronger than SC coupling. The relationship between this behavior and the spin-gap phenomenon is addressed.

Phase diagram of a layered metamagnetic model in the pair approximation

We have studied a layered metamagnetic model in two dimensions through the master equation formalism and by employing the dynamical pair approximation. We have determined the stationary phase diagram of the model and we did not find any evidence for the decomposition of the tricritical point into the critical and bicritical end points as predicted by the mean field theory.

Bicritical points in a nematic rod-disk mixture

The influence of the rod-disk excluded volume on the existence of a bicritical point in a mixture of rodlike and disklike particles has been examined using the second virial theory. Within the approximation in which the interaction kernel is expanded to second order in a basis of symmetry-adapted functions, it is shown from a combination of bifurcation analysis and numerical solution of the Euler-Lagrange equations for the free energy that there exists a value of the rod-disk excluded volume parameter for which the bicritical point disappears.

Critical behavior of uniaxial–biaxial nematic phase transition

A model considering both rodlike molecules and platelike molecules is presented in this paper. The model is treated in the framework of a Landau mean-field theory and renormalization group theory. Mean-field theory predicts the transition between the isotropic, rod nematic, plate nematic, and biaxial nematic phases. The renormalization group analysis shows that the transition exhibits a multiphase bicritical point for n (dimensionality of the order parameter) ⩽2. However, for n>2, the transition exhibits a tetracritical point and an intermediate biaxial nematic phase can exist. The critical exponents are calculated to first order in ε (=4−d).

The three-species monomer-monomer model in the reaction-controlled limit

We study the one dimensional three species monomer-monomer reaction model in the reaction controlled limit using mean-field theory and dynamic Monte Carlo simulations. The phase diagram consists of a reactive steady state bordered by three equivalent adsorbing phases where the surface is saturated with one monomer species. The transitions from the reactive phase are all continuous, while the transitions between adsorbing phases are first-order. Bicritical points occur where the reactive phase simultaneously meets two adsorbing phases. The transitions from the reactive to an adsorbing phase show directed percolation critical behaviour, while the universal behaviour at the bicritical points is in the even branching annihilating random walk class. The results are contrasted and compared to previous results for the adsorption-controlled limit of the same model.

Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions

A monomer-dimer reaction lattice model with lateral repulsion among the same species is studied using a mean-field analysis and Monte Carlo simulations. For weak repulsions, the model exhibits a first-order irreversible phase transition between two absorbing states saturated by each different species. Increasing the repulsion, a reactive stationary state appears in addition to the saturated states. The irreversible phase transitions from the reactive phase to any of the saturated states are continuous and belong to the directed percolation universality class. However, a different critical behavior is found at the point where the directed percolation phase boundaries meet. The values of the critical exponents calculated at the bicritical point are in good agreement with the exponents corresponding to the parity-conserving universality class. Since the adsorption-reaction processes does not lead to a non-trivial local parity-conserving dynamics, this result confirms that the twofold symmetry between absorbing states plays a relevant role in determining the universality class. The value of the exponent $\delta_2$, which characterizes the fluctuations of an interface at the bicritical point, supports the Bassler-Brown's conjecture which states that this is a new exponent in the parity-conserving universality class.

SO(5) invariance and effective field theory for high-Tcsuperconductors

We set up the effective field theories which describe the SO(5)-invariant picture of the high-${T}_{c}$ cuprates in various regimes. We use these to get quantitative conclusions concerning the size of SO(5) breaking effects. We consider two applications in detail: (i) the thermodynamic free energy, which describes the phase diagram and critical behavior, and (ii) the Lagrangian governing the interactions of the pseudo-Goldstone bosons with each other and with the electron quasiparticles deep within the ordered phases. We use these effective theories to obtain predictions for the critical behavior near the possible bicritical point and the pseudo-Goldstone boson dispersion relations, as well as some preliminary results concerning their contribution to response functions. We systematically identify which predictions are independent of the microscopic details of the underlying electron dynamics, and which depend on more model-dependent assumptions.

Mean-field analysis and Monte Carlo study of an interacting two-species reaction model

We study the phase diagram and critical behavior of an interacting one dimensional two species monomer-monomer catalytic surface reaction model with a reactive phase as well as two equivalent adsorbing phase where one of the species saturates the system. A mean field analysis including correlations up to triplets of sites fails to reproduce the phase diagram found by Monte Carlo simulations. The three phases coexist at a bicritical point whose critical behavior is described by the even branching annihilating random walk universality class. This work confirms the hypothesis that the conservation modulo 2 of the domain walls under the dynamics at the bicritical point is the essential feature in producing critical behavior different from directed percolation. The interfacial fluctuations show the same universal behavior seen at the bicritical point in a three-species model, supporting the conjecture that these fluctuations are a new universal characteristic of the model.

Adsorption of a macromolecule in an external field: An exactly solvable model with bicritical behavior

We introduce a model of an adsorbing polymer chain in an external field, which admits exact analytical solution for the partition function for a finite number of the units, $N.$ In the thermodynamic limit, the system has an isotropic and two ordered phases, exhibits continuous and discontinuous phase transitions, and has a bicritical point. We obtain exact expressions for the Landau free energy as a function of an order parameter in the vicinity of the first- and second-order phase transition lines, and compare them to the original theory. The Landau free energy is also calculated as a function of two independent order parameters in the vicinity of the bicritical point. The distribution of complex zeros of the partition function is found for both first- and second-order transitions. In the thermodynamic limit it is described by exact analytical expressions, allowing a comparison to the existing phenomenological results within the framework of the Yang-Lee-Fisher approach. An advantage of the model presented is that the partition function can be calculated analytically not only in the thermodynamic limit, but for finite $N$ as well. The ideas of finite-size scaling analysis are checked against the exact solution, in terms of both the functional form of the free energy and the $N$ dependence of the distribution of Fisher zeros.

Monte Carlo study of the square-lattice annealed Ising model on percolating clusters

Simulations of an Ising $q$-state Potts model which is equivalent to the Ising model on annealed percolation clusters are used to determine the phase diagram of the model in two dimensions. Three topologically different phase diagrams are obtained: (i) for $q=2,$ there are two critical Ising lines meeting at $T=0$ at the four-state Potts critical point; (ii) for $2<q<~4,$ the Ising critical line meets the $q$-state critical line and a line of first-order transitions at a bicritical point; (iii) for $q>4,$ the Ising critical line intersects a line of first-order transitions at a critical end point.

Three-species monomer-monomer model: A mean-field analysis and Monte Carlo study

We study the phase diagram and critical behavior of a one-dimensional three-species monomer-monomer catalytic surface reaction model. Static Monte Carlo simulations are used to roughly map out the phase diagram consisting of a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one monomer species. The transitions from the reactive phase are all continuous, while the transitions between poisoned phases are first order. Of particular interest are the bicritical points where the reactive phase simultaneously meets two poisoned phases. A mean-field cluster analysis fails to predict all of the qualitative features of the phase diagram unless correlations up to triplets of adjacent sites are included. Scaling properties of the continuous transitions and the bicritical points are studied using dynamic Monte Carlo simulations. The transition from the reactive to a saturated phase shows directed percolation critical behavior, while the universal behavior at the bicritical point is in the even branching annihilating random walk class. The crossover from bicritical to critical behavior is also studied.

Neutron-scattering studies of a phase transition in the metamagnetFeBr2under external magnetic fields

Neutron-scattering experiments have been performed on the metamagnet ${\mathrm{FeBr}}_{2}$ under external magnetic fields. We find an anomaly in the temperature (T) and magnetic-field (H) dependences of the intensity of the (2,0,1/2) antiferromagnetic Bragg scattering at the temperature ${\mathrm{T}}_{1}$(H) at which an anomaly in specific heat has been observed in addition to the anomaly at the N\'eel temperature ${\mathrm{T}}_{\mathrm{N}}$(H). We argue that our results are consistent with the theoretical H-T phase diagram of a metamagnet in which the tricritical point decomposes into a critical end point and a bicritical end point. We locate the latter point at ${\mathrm{T}}_{\mathrm{cr}}$\ensuremath{\cong}10.8 K and ${\mathrm{H}}_{\mathrm{cr}}$\ensuremath{\cong}1.4 T in this compound.

Phase diagram of the hard biaxial ellipsoid fluid

The phase diagram of fluids of hard biaxial ellipsoids with c/a=10 and b/a∈{1,10}, where a, b, and c are the semi-axes, has been studied using computer simulation. Four homogeneous phases are in evidence: isotropic (I), nematic (N+), discotic (N−) and biaxial (B). First-order isotropic-nematic and isotropic-discotic coexistence lines have been traced out using Gibbs–Duhem integration of the coexistence pressure with respect to the molecular biaxiality. We conclude that the isotropic-nematic transition is greatly weakened by a modest degree of molecular biaxiality, in agreement with several recent theories. The I–N+ and I–N− lines meet two second-order nematic-biaxial and discotic-biaxial lines at the Landau bicritical point. This point is predicted to occur at around the self-dual particle shape, b/a=c/a, and so extensive simulations have been performed at and around this point. Very sluggish behaviour is expected in this region of the phase diagram and so long simulations were required. An estimate of the location of the Landau bicritical point is reported. We also highlight the asymmetry of the phase diagram about b/a=c/a, where the ellipsoid is neither prolate nor oblate.

A Unified Theory Based on SO(5) Symmetry of Superconductivity and Antiferromagnetism

The complex phase diagram of high-critical temperature (Tc) superconductors can be deduced from an SO(5) symmetry principle that unifies antiferromagnetism and d-wave superconductivity. The approximate SO(5) symmetry has been derived from the microscopic Hamiltonian, and it becomes exact under renormalization group flow toward a bicritical point. This symmetry enables the construction of a SO(5) quantum nonlinear final sigma model that describes the phase diagram and the effective low-energy dynamics of the system. This model naturally explains the basic phenomenology of the high-Tc superconductors from the insulating to the underdoped and the optimally doped region.

Linear theory of Faraday instability in viscous liquids

The linear stability of the plane free surface of a viscous liquid on a horizontal plate under vertical sinusoidal oscillation is analysed theoretically. The free surface of a laterally unbounded liquid of any depth h may always be excited to standing waves if the external acceleration is raised above a critical value a$\_{\text{c}}$. For a fixed external frequency $\omega $, solutions are possible only within certain bands of wave numbers k for a given forcing amplitude above a$\_{\text{c}}$, that is, within tongue-like stability zones in the a-k plane. The analysis for a shallow layer of viscous fluids shows new qualitative behaviours compared to the nearly inviscid theory. It predicts a series of bicritical points, where both harmonic and subharmonic solutions exist for the same forcing amplitude and forcing frequency. This makes harmonic solutions possible at the onset in a laterally large container, which is qualitatively different from the results of nearly inviscid theory. For a low viscosity fluid of small depths, the damping coefficient may be considered proportional to ($\nu \omega $)$^{1/2}$/h in contrast to $\nu \kappa ^{2}$ predicted by the nearly inviscid theory. An approximate analytic expression is derived for the lower part of the lowest marginal curve in cases when the depth of the liquid is much larger than the thickness of the viscous boundary layer formed at the bottom plate. This approximate threshold agrees well with that of recent experiments with viscous liquids.

Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model.

We study a three species monomer-monomer catalytic surface reaction model with a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one species. The transition from the reactive to a saturated phase shows directed percolation critical behavior. Each pair of these reactive-saturated phase boundaries joins at a bicritical point where the universal behavior is in the even branching annihilating random walk class. We find the crossover exponent from bicritical to critical behavior and a new exponent associated with the bicritical interface dynamics.

Equilibrium and kinetic phenomena in a stiff homopolymer and possible applications to DNA

We study the bead-and-spring model of a stiff chain using a self-consistent mean-field approach. For high stiffness parameter the system may undergo a transition to the phase in which the globule acquires a toruslike shape. The phase diagram of the model contains one second- and two first-order transitions meeting at a bicritical point. The stability of the toroidal conformation and scalings of the torus geometry are analyzed. We investigate different kinetic regimes after an instantaneous quench between the extended coil, torus and the spherical globule phases. The kinetic laws that govern these conformational changes are obtained.

Multicritical phenomena for the hydrogen molecule at the large-dimension limit

We show that symmetry breaking of the electronic structure configurations for the Hartree-Fock hydrogen molecule at the large-dimension limit can be described as standard phase transitions. The phase diagram in the internuclear distance-nuclear charge plane shows three different stable phases corresponding to different electronic structure configurations. This phase diagram is characterized by a bicritical point where the two continuous phase transition lines join a first order transition line.

Planform selection in Bénard-Marangoni convection: l hexagons versus g hexagons.

The planform of weakly nonlinear B\'enard-Marangoni convection in a horizontally unbounded layer is analyzed using a combination of direct numerical simulation, amplitude equations, and qualitative discussion. It is demonstrated that there exists a critical Prandtl number ${\mathrm{Pr}}_{\mathit{c}}$ such that in fluids with Pr${\mathrm{Pr}}_{\mathit{c}}$ convection sets in as a pattern of hexagonal cells with downward motion in the center (g hexagons), while for fluids with Prg${\mathrm{Pr}}_{\mathit{c}}$ conventional hexagonal cells with upward motion in the center (l hexagons) appear at the onset of instability. For fluids with Marangoni and Prandtl numbers in the vicinity of the bicritical point (${\mathrm{Ma}}_{\mathit{c}}$,${\mathrm{Pr}}_{\mathit{c}}$) the hexagonal patterns undergo a secondary instability, leading to stationary rolls. The stability domain of stationary rolls increases with the distance from the critical Marangoni number. (c) 1995 The American Physical Society

Competing patterns in the Faraday experiment.

Competition between subharmonically generated equilateral triangles and regular hexagons is observed in the Faraday experiment with viscous fluids subjected to a sinusoidal forcing. For kinematic viscosities around 17 ${\mathrm{cm}}^{2}$/s, all spatially regular patterns---stripes, squares, hexagons, and triangles can be parametrically excited in the same fluid depending on the forcing amplitude and frequency. Close to this value of viscosity, hexagonal and square patterns coexist showing a bicritical point.