Ferromagnetic phases due to competing short- and long-range interactions in the spin-5/2 and spin-2 Blume–Capel model

We broaden the study of the statistical physics of the spin-S Blume–Capel model with ferromagnetic mean-field interactions J in competition with short-range antiferromagnetic interactions K in a linear chain in the thermodynamic limit. This work is dedicated to the case when S takes the half-integer spin $S=5/2$ and when S assumes the integer value $S=2$. In both cases the phase diagrams exhibit new ferromagnetic phases (for certain values of K) enclosed by branches emerging from the first-order frontiers of the pure ferromagnetic model. For finite temperatures the complex topologies were obtained by numerical minimization of the free energy and some results were confirmed by Monte Carlo simulations.     

New Baxter phase in the Ashkin–Teller model on a cubic lattice

The mean field theory results are obtained from the Bogoliubov inequality for the spin-1/2 Ashkin–Teller model on a cubic lattice for different cluster sizes. The phase diagram, magnetization and free energy are obtained. From those expressions we observed a new phase in the model. Denoted in the course of this work by Baxter⁽²⁾ this new phase presents $〈S〉\ne 〈\sigma 〉\ne 0$. The phase transitions between the Baxter⁽²⁾ and the others well known phases for the model are studied and classified.     

The spin-1 Blume–Capel model on the Bethe lattice in ± J distribution with an adjustable parameter between FM and AFM phases

The spin-1 Blume–Capel (BC) model is studied on the Bethe lattice (BL) for the ?±? J distribution with a competing adjustable parameter α which alters the strength of bilinear exchange interaction parameter for the ferromagnetic phase (J?>?0) with respect to antiferromagnetic phase (J?<?0). The J?>?0 and αJ?<?0 values are also distributed throughout the BL with probabilities p and $1?p,$ respectively. The order-parameters are obtained on the BL in terms of exact recursion relations (ERR’s) and their temperature (T) variations are studied to calculate the phase diagrams on the (α, T) planes for given values of p, crystal field (D) and coordination number $q=3$ corresponding to honeycomb lattice. It is found that the model gives both first- and second-order phase transitions and also tricritical points. In addition to the well known ordinary phases and TCP’s, the spin glass phase and two more special points are also observed.     

Triangle for the entropic index q of non-extensive statistical mechanics observed by Voyager 1 in the distant heliosphere

Tsallis [Physica A 340 (2004) 1) identified a set of numbers, the “q-triplet” ≡ {q_stat, q_sen, q_rel}, for a system described by non-extensive statistical mechanics. The deviation of the q's from unity is a measure of the departure from thermodynamic equilibrium. We present observations of the q-triplets derived from two sets of daily averages of the magnetic field strength B observed by Voyager 1 in the solar wind near 40 A.U. during 1989 and near 85 A.U. during 2002, respectively. The results for 1989 do not differ significantly from those for 2002. We find $q_{\mathrm{stat}}=1.75\pm 0.06$, $q_{\mathrm{sen}}=-0.6\pm 0.2$, and $q_{\mathrm{rel}}=3.8\pm 0.3$.     

Nonlinear integral equations for the finite size effects of RSOS and vertex-models and related quantum field theories

Starting from critical RSOS lattice models with appropriate inhomogeneities, we derive two component nonlinear integral equations to describe the finite volume ground state energy of the massive ${\varphi }_{\mathrm{id},\mathrm{id},\mathrm{adj}}$ perturbation of the $\mathit{SU}{(2)}_k\times \mathit{SU}{(2)}_{k^{\prime }}/\mathit{SU}{(2)}_{k+k^{\prime }}$ coset models. When $k^{\prime }\to \infty$ while the value of k is fixed, the equations correspond to the current–current perturbation of the $\mathit{SU}{(2)}_k$ WZW model. Then modifying one of the kernel functions of these equations, we propose two component nonlinear integral equations for the fractional supersymmetric sine-Gordon models. The lattice versions of our equations describe the finite size effects in the corresponding lattice models, namely in the critical $\mathrm{RSOS}(k,q)$ models, in the isotropic higher-spin vertex models, and in the anisotropic higher-spin vertex models. Numerical and analytical checks are also performed to confirm the correctness of our equations. These type of equations make it easier to treat the excited state problem.     

Enhanced energy storage and pyroelectric properties of highly (100)-oriented (Pb1−x−yLaxCay)Ti1−x/4O3 thin films derived at low temperature

Highly (100)-oriented (Pb_1?x?yLa_xCa_y)Ti_1?x/4O₃ ($x=0.15$, $y=0.05$; $x=0.1$, $y=0.1$; $x=0.05$, $y=0.15$) thin films were deposited on Pt/Ti/SiO₂/Si substrates at a low temperature of 450?°C via a sol–gel route. It was found that all the (Pb_1?x?yLa_xCa_y)Ti_1?x/4O₃ thin films could be completely crystallized and the content of La/Ca showed a significant effect on the electrical properties of films. Among the three films, the (Pb_1?x?yLa_xCa_y)Ti_1?x/4O₃ ($x=0.1$, $y=0.1$) thin film exhibited the enhanced overall electrical properties, such as a low dielectric loss ($\tan ?\delta <0.08$) and leakage current ($J～4.6\times {10}^{?5}$ A/cm²), a high recoverable energy density (W_re ～ 15 J/cm³), as well as a large pyroelectric coefficient (p ～ 190 μC/m²K) and figure of merit ($F_{\mathrm{d}}^{\prime }～77\mathrm{\mu }\text{C}/{\text{m}}^2$K). The findings suggest that the fabricated thin films with a good (100) orientation can be an attractive candidate for applications in Si-based energy storage and pyroelectric devices.     

First-principles study on the phase transitions,crystal stabilities and thermodynamic properties of TiN under high pressure

The structural and thermodynamic properties of titanium nitride (TiN) have been investigated by merging first-principles calculations and particle-swarm algorithm. The three phases are identified for TiN, including the B1, the $P{6}_3/mmc$, and the B2 phases. A new phase of anti-TiP structure with the space group $P{6}_3/mmc$ has been predicted. The calculated phase transition from the B1 to the $P{6}_3/mmc$ occurs at 270 GPa. The vibrational, elastic, and thermodynamic properties for the three phases have been calculated and discussed.     

New R-matrices from representations of braid-monoid algebras based on superalgebras

In this paper we discuss representations of the Birman–Wenzl–Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to derive novel trigonometric solutions of the graded Yang–Baxter equation. In this way we obtain the multiparametric R-matrices associated to the $U_q[\mathit{sl}{(r|2m)}^{(2)}]$, $U_q[\mathit{osp}{(r|2m)}^{(1)}]$ and $U_q[\mathit{osp}{(r=2n|2m)}^{(2)}]$ quantum symmetries. Two other families of multiparametric R-matrices not predicted before within the context of quantum superalgebras are also presented. The latter systems are indeed non-trivial generalizations of the $U_q[D_{n+1}^{(2)}]$ vertex model when both distinct edge variables statistics and extra free-parameters are admissible.