Multicritical Behavior Research Articles

Anisotropic Ashkin-Teller Model in a Transverse Field

Magnetic properties and phase diagrams of a spin-1/2 anisotropic Ashkin-Teller model in a transverse field are studied using the mean field theory. On the one hand, it is found that there exists a critical value of the transverse field Ωc/J1 above which the partially ordered phase 〈σS〉 appears at very low temperature and sufficiently large values of the four-spin interaction coefficient J4/J1. Such result is not obtained in the Ω/J1 = 0 case. On the other hand, the multicritical behaviour is also studied as a function of the transverse field Ω/J1 for selected values of the spin interaction coefficient J2/J1. However, depending on the transverse field value, and a fixed J2/J1 value, four varieties of phase diagrams are found. General formulae are established for an arbitrary coordination number q. The phase diagrams and the behaviour of the transverse and longitudinal magnetisations are given for q = 4.

Tricritical behavior of compressible systems with frozen-in structure defects

A field-theoretical description of phase transformations in weakly disordered elastically isotropic compressible systems is given. For three-dimensional Ising-like systems in a two-loop approximation, renormalization-group equations were analyzed using the Pade-Borel technique of summing and fixed points were distinguished that correspond to various types of critical and tricritical behavior under various macroscopic conditions imposed on the system. It is shown that a significant effect on the critical and tricritical behavior of compressible systems is exerted by structural defects, which manifests itself in both a change in the magnitudes of critical exponents and a decrease in the number of various types of multicritical behavior in comparison with uniform compressible systems.

Renormalization group analysis of tachyon condensation

Renormalization group analysis of boundary conformal field theory on bosonic D25-brane is used to study tachyon condensation. Placing the lump on a finite circle and triggering only the first three tachyon modes, the theory flows to nearby IR fixed point representing lumps that are extended object with definite profile. The boundary entropy corresponding to the D24-brane tension is calculated in the leading order in perturbative analysis which decreases under RG flow and agrees with the expected result to an accuracy of 8%. Multicritical behaviour of the IR theory suggests that the end point of the flow represents a configuration of two D24-branes. Analogy with Kondo physics is discussed.

Random-bond Ising model in two dimensions: The Nishimori line and supersymmetry

We consider a classical random-bond Ising model (RBIM) with binary distribution of $\pm K$ bonds on the square lattice at finite temperature. In the phase diagram of this model there is the so-called Nishimori line which intersects the phase boundary at a multicritical point. It is known that the correlation functions obey many exact identities on this line. We use a supersymmetry method to treat the disorder. In this approach the transfer matrices of the model on the Nishimori line have an enhanced supersymmetry osp($2n+1|2n$), in contrast to the rest of the phase diagram, where the symmetry is osp($2n|2n$) (where $n$ is an arbitrary positive integer). An anisotropic limit of the model leads to a one-dimensional quantum Hamiltonian describing a chain of interacting superspins, which are irreducible representations of the osp($2n+1|2n$) superalgebra. By generalizing this superspin chain, we embed it into a wider class of models. These include other models that have been studied previously in one and two dimensions. We suggest that the multicritical behavior in two dimensions of a class of these generalized models (possibly not including the multicritical point in the RBIM itself) may be governed by a single fixed point, at which the supersymmetry is enhanced still further to osp($2n+2|2n$). This suggestion is supported by a calculation of the renormalization-group flows for the corresponding nonlinear sigma models at weak coupling.

Multicritical points in the mixed spin-1 and spin- [formula omitted] Ising system on a square lattice with different single-ion anisotropies

Using an effective-field theory we study a multicritical behaviour of the mixed spin-1 and spin- 3 2 Ising model with different anisotropies on a square lattice. We find a variety of topologies of the finite-temperature phase diagrams, with several multicritical points. The highest-order multicritical entity is the fourth-order point, which contradicts earlier results obtained within the same theoretical framework.

Multicritical behavior of the phase diagrams of ferromagnet/superconductor layered structures

For ferromagnet/superconductor (F/S) layered structures, new 3D Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states are predicted. In most cases, these states are characterized by a higher critical temperature Tc than the known 1D LOFF states. It is shown that the nonmonotonic behavior of Tc is determined by the oscillations of the Cooper pair flux through the F/S boundary, which occur as a result of the 3D-1D-3D phase transitions at the Lifshits triple points. The appearance of the new 3D LOFF states and the presence of nonmagnetic impurities leads to a strong damping of the 1D oscillations of the LOFF pair amplitude and to a considerable smoothing of the dependence of Tc on the F layer thickness df. An interpretation of the behavior of the experimental dependences Tc(df) obtained for F/S structures is proposed.

Numerical study of a lattice-gas model for micellar binary solutions

Two nonperturbative methods such as transfer-matrix finite-size scaling and Monte Carlo simulations are used to investigate the multicritical behavior of a lattice-gas model proposed by Shnidman and Zia [J. Stat. Phys 50, 839 (1988)] for studying the micellar binary solutions of water and amphiphile. The phase diagrams are obtained in both the magnetic field-temperature (H,T) and amphiphile density temperature $({\ensuremath{\rho}}_{s},T)$ for different values of competing interactions ${(K}_{0}$ and ${K}_{1})$ and in the presence of the attraction interaction intermicellar parameter (J). Our nonperturbative results are compared with previous mean-field ones. Both methods confirm the absence of the rarefied micelle at high temperature as found previously by mean-field calculations. Also our phase diagrams present transitions of first- and second-order transitions linked by tricritical and multicritical points of higher order. Finally, with the use of finite-size-scaling ideas, the critical exponents have been calculated. Our results show that this model has a nonuniversal behavior that belongs to the XY model with cubic anisotropy for a certain range of interactions parameters and a universal behavior that belongs to the $d=2$ Ising model.

Multicritical behavior of disordered systems with two order parameters

A field-theoretic description of phase transitions in disordered systems with two coupled order parameters is given. An analysis of renormalization-group functions is performed directly for three-dimensional systems in a two-loop approximation by using the Pade-Borel summation technique. Fixed points are found corresponding to stable multicritical behavior. The effect of frozen point impurities on the phase diagrams of the system is studied.

Multicritical behavior of weakly disordered systems with two order parameters

We present a field-theoretic description of phase transitions in weakly disordered systems with two coupled order parameters. Using the two-loop approximation and the Pade-Borel summation technique, we carry out a renormalization-group analysis of the scaling functions for three-dimensional systems and identify the fixed points corresponding to stable multicritical behavior. We also study the effect of frozen point impurities on the nature of the phase diagrams.

Nonequilibrium critical behavior in unidirectionally coupled stochastic processes.

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d(c)=4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A-->A+A, A+A-->A, and A-->0. We study a hierarchy of such DP processes for particle species A,B,..., unidirectionally coupled via the reactions A-->B, ...(with rates mu(AB),...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents beta(i) which are markedly reduced at each hierarchy level i> or =2. This scenario can be understood on the basis of the mean-field rate equations, which yield beta(i)=1/2(i-1) at the multicritical point. Using field-theoretic renormalization-group techniques in d=4-epsilon dimensions, we identify a new crossover exponent phi, and compute phi=1+O(epsilon(2)) in the multicritical regime (for small mu(AB)) of the second hierarchy level. In the active phase, we calculate the fluctuation correction to the density exponent on the second hierarchy level, beta(2)=1/2-epsilon/8+O(epsilon(2)). Outside the multicritical region, we discuss the crossover to ordinary DP behavior, with the density exponent beta(1)=1-epsilon/6+O(epsilon(2)). Monte Carlo simulations are then employed to confirm the crossover scenario, and to determine the values for the new scaling exponents in dimensions d< or =3, including the critical initial slip exponent. Our theory is connected to specific classes of growth processes and to certain cellular automata, and the above ideas are also applied to unidirectionally coupled pair annihilation processes. We also discuss some technical as well as conceptual problems of the loop expansion, and suggest some possible interpretations of these difficulties.

Multicritical behavior in ferroelectrics

Solid state systems exhibit besides usual second order phase transitions a rich variety of multicritical phenomena like Lifshitz points (or lines), tricritical points (or lines) and even tricritical Lifshitz points. Realizations of such points are numerous and were also verified in the family of ferroelectrics of the type (PbySn1y)2P2(SexS1-x)6. A review of the critical behavior at such points is presented here. Because of the importance of the uniaxial dipolar interaction in ferroelectrics the critical behavior is different from systems with short range interaction only. Moreover the coupling to the elastic degrees of freedom may not be neglected, and leads under certain conditions to a critical temperature dependence in certain elastic constants. Crossover phenomena, which are expected in the experimental accessible region of experiments are also considered.

Field-theoretic description of the multicritical behavior of systems with two order parameters

A field-theoretic description of phase transformations in complex systems with two interacting order parameters is given. For three-dimensional systems in the two-loop approximation a renormalization-group analysis of the scaling functions is carried out directly, and the fixed points corresponding to stability of the bicritical and tetracritical behavior are identified. The critical exponents at the multicritical points in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.

Comment on “Multicritical Behavior in Coupled Directed Percolation Processes”

A Comment on the Letter by Uwe C. T{umlt a}uber, Martin J. Howard, and Haye Hinrichsen, Phys.thinspthinspRev.thinspthinspLett.thinspthinsp{bold 80}, 2165 (1998). The authors of the Letter offer a Reply. {copyright} {ital 1998} {ital The American Physical Society}

3D XY scaling theory of the superconducting phase transition

The intermediate 3D XY scaling theory of superconductivity at zero and nonzero magnetic fields is developed, based only upon the dimensional hypothesis B∼(Length) −2. Universal as well as nonuniversal aspects of the theory are identified, including background terms and demagnetization effects. Two scaling regions are predicted: an `inner' region (very near the zero field superconducting transition, T c), where the fields B, H, and H ex differ substantially, due to the presence of diamagnetic fluctuations; and an `outer' region (away from T c), where the fields can all be treated similarly. The characteristic field ( H 0) and temperature ( t 1) scales, separating the two regimes, are estimated. Scaling theories of the phase transition line, magnetization, specific heat, and conductivity are discussed. Multicritical behavior, involving critical glass fluctuations, is investigated along the transition line, T m( B), at nonzero fields.

Phase diagrams, critical, and multicritical behavior of hard-core Bose-Hubbard models

We determine the zero-temperature phase diagram of the hard-core Bose-Hubbard model on a square lattice by mean-field theory supplemented by a linear spin-wave analysis. Due to the interplay between nearest and next-nearest neighbor interaction and cubic anisotropy several supersolid phases with checkerboard, stripe domain or intermediate symmetry are stabilized. The phase diagrams show three different topologies depending on the relative strength of nearest and next-nearest neighbor interaction. We also find a rich variety of new quantum critical behavior and multicritical points and discuss the corresponding effective actions and universality classes.

Multicritical microscopic spectral correlators of hermitian and complex matrices

We find the microscopic spectral densities and the spectral correlators associated with multi-critical behavior for both hermitian and complex matrix ensembles, and show their universality. We conjecture that microscopic spectral densities of Dirac operators in certain theories without spontaneous chiral symmetry breaking may belong to these new universality classes.

Multicritical Behavior in Coupled Directed Percolation Processes

We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents \beta^{(k)} which are markedly reduced at each hierarchy level k >= 2. We compute the fluctuation corrections to \beta^{(2)} to O(\epsilon = 4-d) using field-theoretic renormalization group techniques. Monte Carlo simulations are employed to determine the new exponents in dimensions d <= 3.

Magnetic susceptibility measurements near the multicritical point of the spin-reorientation transition in ultrathin fcc Fe(111)/2 ML Ni/W(110) films

Iron films grown on a two-monolayer Ni/W(110) substrate undergo a temperature-driven spin reorientation which can be followed experimentally from a low-temperature, perpendicularly magnetized monodomain state all the way to the high-temperature paramagnetic state without a significant change of the atomic structure. Measurements of the magnetic susceptibility, using the magneto-optic Kerr effect, give the entire temperature vs thickness phase diagram for the spin reorientation, including measurements close to the multicritical point where the reorientation and Curie temperatures are equal. The technique is particularly sensitive to the formation of the perpendicularly magnetized domains associated with the spin reorientation and reveals that films with a thickness in the neighborhood of the multicritical behavior also display a maximum in the temperature at which domain formation begins. Thinner films undergo the transition from ferromagnetic-to-paramagnetic behavior directly from the domain state, but no signature of the critical temperature itself is seen in the magnetic susceptibility.

Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process

A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well known exponents of Reggeon field theory. In addition this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.

Critical behavior of the three-dimensional Ising model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions

The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the recently proposed cluster variation--Pad\'eapproximant method. Particular attention is paid to the line of critical end points of the ferromagnetic-paramagnetic phase transition: its (multi)critical exponents are calculated, and their values suggest that the transition belongs to a different universality class. A rough estimate of the crossover exponent is also given.