Phase Transitions of a Dilute O(n) Model

We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of the lattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix. Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of the Ising point, the tricritical line extends to the n=2 point describing a tricritical O(2) model.     

Tricritical Directed Percolation

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations. PACS numbers: 05.70.Ln, 05.50.+q, 05.65.+b     

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Revisiting the nonequilibrium phase transition of the triplet-creation model

The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition becomes discontinuous. As the diffusion probability increases the critical exponents change continuously from the ordinary directed percolation (DP) class to the compact directed percolation (CDP). The fractal dimension of the critical cluster, however, switches abruptly between those two universality classes. Strong crossover effects in both methods make it difficult, if not impossible, to establish the exact location of the tricritical point.     

Fractal structure of high-temperature graphs of O(N) models in two dimensions

The critical behavior of the two-dimensional O(N) model close to criticality is shown to be encoded in the fractal structure of the high-temperature graphs of the model. Based on Monte Carlo simulations and with the help of percolation theory, de Gennes' results for polymer rings, corresponding to the limit N-->0, are generalized to random loops for arbitrary -2相似文献   

Stationary State Solutions of a Bond Diluted Kinetic Ising Model: An Effective-Field Theory Analysis

We examined the stationary state solutions of a bond diluted kinetic Ising model under a time dependent oscillating magnetic field within the effective-field theory (EFT) for a honeycomb lattice (q=3). The effects of the Hamiltonian parameters on the dynamic phase diagrams have been discussed in detail. Bond dilution process on the kinetic Ising model causes a number of interesting and unusual phenomena such as reentrant phenomena and has a tendency to destruct the first-order transitions and the dynamic tricritical point. Moreover, we have investigated the variation of the bond percolation threshold as functions of the amplitude and frequency of the oscillating field.     

Percolation Phase Transitions from Second Order to First Order in Random Networks

We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 qc 0.25 separating the two phase transition types.     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

Adsorbing and Collapsing Directed Animals

A model of a self-interacting directed animal, which also interacts with a solid wall, is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition. The directed animal is confined to a 45° wedge, and it interacts with one of the walls of this wedge. The existence of a thermodynamic limit in this model shown, and the presence of an adsorption transition is demonstrated by using constructive techniques. By comparing this model to a process of directed percolation, we show that there is also a collapse or -transition in this model. We examine directed percolation in a wedge to show that there is a collapse phase present for arbitrary large values of the adsorption activity. The generating function of adsorbing directed animals in a half-space is found next from which we find the tricritical exponents associated with the adsorption transition. A full solution for a collapsing directed animal seems intractible, so instead we examine the collapse transition of a model of column convex directed animals with a contact activity next.     

On the growth of percolation clusters: The effects of time correlations

We discuss the effects of the time correlations in the choice of growth sites for percolation clusters in two dimensions. To this end, we study two well-defined models: (i) FIFO (First-In, First-Out), in which the next-cluster growth site is theoldest, and (ii) FILO (First-In, Last-Out), where the next cluster growth site to be chosen is thenewest. We find that FIFO and FILO have dramatically differentkinetic exponents, even though thestatic exponents are the same (viz., percolation exponents). We find that the percolation thresholdp _c is analogous to the point of a linear polymer, and we develop the corresponding tricritical point scaling relations.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Absence of the small tricritical deviation from the mean-field approximation for the isotropic-nematic phase transition

The tricritical behaviour of the isotropic-nematic phase transition is studied. The presence of two independent sixth-order terms in the free energy expansion breaks the conventional tricritical behaviour and eliminates the tricritical restriction for the deviation from the mean-field approximation.     

Finite size scaling approach to a metamagnetic model in two dimensions

We investigate the tricritical properties of a metamagnetic model, namely the next-nearest neighbor Ising antiferromagnet, in two dimensions. We calculate the transfermatrix on finite strips and use finite size scaling to obtain the critical line. The tricritical point and its exponents are obtained by two different methods. In the case of strong intersublattice coupling no evidence for tricritical behavior is found.     

An exactly soluble model with tricritical points for structural-phase transitions

We present and study a lattice-dynamical model whose static and dynamic properties can be described exactly for all dimensionsd≧3 (d an integer) and which, in addition, exhibits tricritical points. For certain model parameters, the tricritical behaviour is found to be identical to that of the spherical model. By changing the model parameters continuously however, the transition suddenly becomes of first order at a tricritical point (TCP). The order parameter and the susceptibility are given explicitly ford≧3. The tricritical exponents are Gaussian. The critical dynamics is also discussed.     

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions.     

Critical Properties of Anisotropic Heisenberg Ferromagnet with Spin-One

Combining the two-site cluster approximation with the discretized path-integral representation (DPIR) and Suzuki-Trotter formalism, the critical properties of anisotropic Heisenberg ferromagnet with a crystal field are studied. We find that the tricritical point can appear in the case of negative crystal field. And the exchange anisotropy not only reduces the critical temperature and tricritical point, but also makes re-entrant phenomena instead of the existence of the tricritical point when the exchange anisotropic parameter is larger than a critical value.     

The Landau theory and the tricritical point

We show from the Landau theory of the tricritical point that the transition line has not necessarily a continuous slope and that it is possible to find behavior analogous to those of the tricritical points of first and second kind, analyzed by Reatto.     

Effect of elastic deformations on the critical behavior of disordered systems with long-range interactions

A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter. Renormalization-group equations are analyzed in the two-loop approximation by using the Padé-Borel summation technique. The fixed points corresponding to critical and tricritical behavior of the systems are determined. Elastic deformations are shown to changes in critical and tricritical behavior of disordered compressible systems with long-range interactions. The critical exponents characterizing a system in the critical and tricritical regions are determined.     

A systematic approach to the calculation of tricritical temperature with application to the nematic-smecticA phase transition

Using the Landau expansion equations have been found that allow for systematic calculations of tricritical temperature for a given molecular model. The theory has been applied to nematic-smecticA (NA) phase transition of liquid crystals. It has been shown exactly that the NA tricritical temperature depends only on the couplings between the two lowest order translational order parameters and the orientational degrees of freedom. Numerical results of Mayer and Lubensky for the NA tricritical point have been derived exactly. Also a stability condition of the obtained solution has been discussed.Alexander von Humboldt Foundation Fellow, 1985–1986     

Nonclassical equations of state for critical and tricritical points

We develop a method by which certain classical equations of state may be modified to produce nonclassical critical scaling behavior. We then apply this method to the classical free energy describing a tricritical point that was originally introduced by Griffiths. The phase behavior of the resulting nonclassical free energy is characterized by the competition between critical scaling and tricritical scaling already envisioned by previous authors.Work supported by the National Science Foundation and the Cornell University Materials Science Center.Footnotes 3–10 of Ref. 1 provide a comprehensive list of experimental investigations of tricritical points in fluid mixtures.