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.     

Laser-phase transition analogy: Tricritical points

It is shown that laser behavior near threshold displays the non-equilibrium analogue of a tricritical point in the (E, S, δ) phase space, where E is the field; S, the injected signal; and δ, the population inversion. These tricritical points appear easily accessible to experiments of the form done by Chebotayev et al. with saturable absorbers.     

Scaling laws connecting tricritical and normal critical exponents for dimensionsd≦3

The method of Imry, Deutscher, Bergman and Alexander for deriving interdimensional scaling laws is used in a modified form to establish scaling relations between tricritical and normal critical exponents. These relations are expected to hold for dimensionsd≦ 3. The tricritical behaviour ford=3 andd>3 has previously been discussed by Wegner and Riedel and by the author.     

Tricritical phase transitions in semi-infinite systems

Semi-infinite systems with a bulk tricritical point are studied using a free energy functional of the Ginzburg-Landau-Wilson type. Tricritical surface exponents, order parameter profiles and the phase diagram are presented within mean field theory. In the case of ordinary and special transition, renormalization-group methods are used to obtain the exponents of a system withO(n)-symmetry to first order in ?=3?d and logarithmic corrections ind=3.     

Integrable aspects of the scaling q-state Potts models II: finite-size effects

We continue our discussion of the q-state Potts models for q⩽4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated; here, we consider finite-size behaviour. TBA equations are proposed for all cases related to φ₂₁ and φ₁₂ perturbations of unitary minimal models. These are subjected to a variety of checks in the ultraviolet and infrared limits, and compared with results from a recently-proposed non-linear integral equation. A non-linear integral equation is also used to study the flows from tricritical to critical models, over the full range of q. Our results should also be of relevance to the study of the off-critical dilute A models in regimes 1 and 2.     

Nonlocality and l dependence of the phonon frequencies of lithium

Phonon frequencies of lithium have been computed by using the Shaw optimized nonlocal model potential with Shaw, Singwi et al. and q-independent exchange and correlation factors. It is found that the feature of cross-over observed by Smith et al. along [100] direction is not related to either nonlocality or modelling for l=1, but to the form of exchange and correlation. It is suggested that _χ appearing in the Shaw or Singwi et al. forms of screening should be less dependent on q.     

q-bosons and the Lie-deformed Heisenberg algebra

It is shown that the non-Hermitian realization of a Lie-deformed Heisenberg algebra given by Jannussis et al. is closely related with the q-Heisenberg-Weyl algebra of Biedenharn and Macfarlane with q being a phase (q = e^iθ, with θ real). The physical implications of this result are stressed.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

Series expansions for a generalized XY hamiltonian: II. Tricritical behaviour of the Takagi model

The high-temperature series expansions for the square of the fluctuation in the order parameter, for the specific heat, the concentration and the concentration susceptibility for the Takagi model on an f.c.c. lattice are analysed in the field variables. We obtain for the critical exponent $\text{γ =}\text{4}\text{3}$ and the specific heat is possibly logarithmically divergent. If we take the tricritical point to be determined by γ_t = 1, the tricritical exponents α_t, λ_t and ω_t are found to be consistent with $\text{1}\text{2}$.     

Tricritical point of the three-dimensional Potts model (q = 4) with quenched nonmagnetic disorder

The effect of quenched nonmagnetic impurities on the phase transitions in the three-dimensional Potts model with the number of spin states q = 4 for the case of the simple cubic lattice is studied using the Monte Carlo method. The phase transitions in this model are studied for spin density p ranging from 1.0 to 0.70. The position of the tricritical point at the phase diagram is determined.     

The phase-transition order parameter, fluctuations, and nanoclusters in benzil crystals

Bragg and diffuse X-ray reflections from the M points of the Brillouin zone boundary of a benzil crystal paraphrase, the integral intensity of which is associated with the order parameter and its fluctuations, are studied. Original data on the temperature behavior of the order parameter and diffuse scattering are obtained. The relevant critical exponents are determined. A conclusion is drawn as to the proximity of the phase transition in these crystals to the tricritical point. A phase transition model is discussed.     

First-order phase transitions and integrable field theory. The dilute q-state Potts model

We consider the two-dimensional dilute q-state Potts model on its first-order phase transition surface for 0 < q ⩽ 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of the dilution, thermal and spin operators. They provide an approximation for the correlation functions whose accuracy is illustrated by evaluating the central charge and the scaling dimensions along the tricritical line.     

Orientational structures in nematic droplets with conical boundary conditions

Slightly diluted magnetic systems described by the disordered three-dimensional Potts model with the number of spin states q = 3 are studied in the case of a simple cubic lattice. The position of the tricritical point in the phase diagram is determined using the histogram Monte Carlo technique.     

The random field Ising model with an asymmetric trimodal probability distribution

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(h_i)=pδ(h_i−h₀)+qδ(h_i+h₀)+rδ(h_i), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), h_i is the random field variable and h₀ the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h₀, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

Identities for Sums of a q-Analogue of Polylogarithm Functions

A q-analogue of the polylogarithm function is introduced via a consideration of the spectral zeta-function of the quantum group SU _q (2). We derive certain identities for linear and non-linear combinations of the q-analogue of polylogarithm functions with negative exponents.     

Analytic determination of the T-μ phase diagram of the chiral quark model

Using a gap equation for the pion mass a non-perturbative method is given for solving the chiral quark-meson model in the chiral limit at the lowest order in the fermion contributions encountered in a large-N _fapproximation. The location of the tricritical point is analytically determined. A mean field potential is constructed from which critical exponents can be obtained.     

Coupled minimal models with and without disorder

We analyze in this article the critical behavior of M q₁-state Potts models coupled to N q₂-state Potts models (q₁, q₂ ε [2, …, 4]) with and without disorder. The techniques we use are based on perturbed conformal theories. Calculations have been performed at two loops. We already find some interesting situations in the pure case for some peculiar values of M and N with new tricritical points. When adding weak disorder, the results we obtain tend to show that disorder makes the models decouple. Therefore, no relations emerges, at a perturbation level, between for example the disordered q₁ × q₂-state Potts model and the two disordered q₁, q₂-state Potts models (q₁ ≠ q₂), despite the fact that their central charges are similar according to recent numerical investigations.     

Comment on a recent calculation of the Ham's reduction factors by the use of the exponential transformation method

The reduction factors p and q for an E electronic state with linear Jahn-Teller coupling to an E vibrational mode have been calculated numerically. The results together with other evidence suggest that the results obtained by Sigmund et al. using the transformation method are incorrect in the intermediate and strong coupling regimes.