Interplay between spin frustration and thermal entanglement in the exactly solved Ising–Heisenberg tetrahedral chain

The spin-1/2 Ising–Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry (the total spin of the Heisenberg bonds is locally conserved) and the transfer-matrix approach. Exact results derived for spin–spin correlation functions are employed to obtain the frustration temperature. In addition, we have exactly calculated a concurrence quantifying thermal entanglement. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations.     

Macroscopic ground-state degeneracy and magnetocaloric effect in the exactly solvable spin-1/2 Ising–Heisenberg double-tetrahedral chain

The ground-state degeneracy and magnetocaloric effect in the spin-1/2 Ising–Heisenberg double-tetrahedral chain are exactly investigated. It is demonstrated that the zero-temperature phase diagram involves two classical and two quantum chiral phases with distinct degrees of the macroscopic degeneracy. Different macroscopic degeneracies observed in the latter phases and at individual ground-state phase transitions are confirmed by multiple-peak dependencies of the specific heat and entropy on the magnetic field. The cooling capability of the model is well illustrated by the magnetic-field variations of the isothermal entropy change, temperature isotherms and the magnetic Grüneisen parameter.     

The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising–Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal D_z and transverse D_x crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second-and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.     

Critical and Tricritical Wetting in the Two-Dimensional Blume–Capel model

The two-dimensional Blume–Capel model with free surfaces where a surface field \(H_1\) acts and the “crystal field” (controlling the density of the vacancies) takes a value \(D _s\) different from the value \(D\) in the bulk, is studied by Monte Carlo methods. Using a recently developed finite size scaling method that studies thin films in a \(L \times M\) geometry with antisymmetric surface fields \((H_L=-H_1)\) and keeps a generalized aspect ratio \(c = L^2/M\) constant, surface phase diagrams are computed for several typical choices of the parameters. It is shown that both second order and first order wetting transitions occur, separated by tricritical wetting behavior. The special role of vacancies near the surface is investigated in detail.     

Entanglement detection in the mixed-spin Ising–XY model

In the present work, we initially verify anisotropy effect on the heat capacity of a mixed-three-spin(1/2,1,1/2) system(where spins(1/2,1/2) have XY interaction and spins(1,1/2) have Ising interaction together) at finite temperatures, then,the pairwise entanglement for spins(1/2,1/2), by means of negativity(as a measure of entanglement) as a function of the temperature T, homogeneous magnetic field B, and anisotropy parameter γ is investigated. In addition, we show that one can find magnetic phase transition points for the spins(1/2,1/2) at finite temperatures and understand properly their behavior with respect to the magnetic field and the anisotropy parameter, via the negativity function. An interval of the magnetic field from the negativity diagram of the spins(1/2,1/2) is presented in which quantum phase transition occurs for the tripartite mixed-three-spin system. Finally, some new interesting entanglement witnesses are introduced by using non-degenerate perturbation theory for the mixed-three-spin system.     

Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass

Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.     

Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models

Renormalization group based on the Migdal–Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical models. In presence of quenched disorder, however, predictions obtained with the Migdal–Kadanoff bond removal approach quite often fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In an attempt to overcome this limitation we analyze the behavior of Ising and Blume–Emery–Griffiths models on more structured hierarchical lattices. We find that, apart from some exceptions, the failure is not limited to Midgal–Kadanoff cells but originates right from the hierarchization of Bravais lattices on small cells, and shows up also when in-cell loops are considered.     

Λ and the Heisenberg Principle

A time dependent “cosmological constant” Λ(t) is conjectured, in terms of the Gaussian curvature of the causal horizon. It is nonvanishing even in Minkowski space because of the lack of informations beyond the light cone. Using the Heisenberg Principle, the corresponding energy of the quantum fluctuations localized on the past or future null horizons is proportional to Λ^1/2. We compute Λ(t) for the (Lorenzian version) of the (conformally flat) Hawking wormhole geometry (written in static spherical Rindler coordinates) and for the de Sitter spacetime. A possible explanation of the Hawking temperature is proposed, in terms of a constant Λ.     

Critical gravity in the Chern–Simons modified gravity

We perform the perturbation analysis of the Chern–Simons modified gravity around the AdS₄ spacetime (its curvature radius ℓ) to obtain the critical gravity. In general, we could not obtain an explicit form of perturbed Einstein equation which shows a massive graviton propagation clearly, but for the Kerr–Schild perturbation and Chern–Simons coupling θ=kx/y, we find the AdS wave as a single massive solution to the perturbed Einstein equation. Its mass squared is given by M ²=[−9+(2ℓ ²/k−1)²]/4ℓ ². At the critical point of M ²=0 (k=ℓ ²/2), the solution takes the log-form and the linearized excitation energies vanish.     

A Remark on the Residual Entropy of the Antiferromagnetic Ising Model in the Maximal Critical Field

By means of a transfer matrix method, we show that the residual entropy S of the two-dimensional square lattice antiferromagnetic Ising model in the maximal critical field satisfies (ln λ _n )/(n+1)≤S≤(ln λ _n )/n, where λ _n is the largest eigenvalue of the transfer matrix F _n on a strip of width n. Using these bounds, we numerically calculate the value of S, with precise estimates on the errors, namely, S=0.394198±0.020747.     

Hysteresis and avalanches in the site-diluted Ising model: comparison with experimental results in Cu–Al–Mn alloys

We study the zero temperature properties of hysteresis in a site-diluted Ising model. The model exhibits a critical line separating a disordered from an incipient ferromagnetic ground state: the shape of the hysteresis loop changes from a smooth cycle (formed as a sequence of tiny avalanches) to a sharp cycle exhibiting a macroscopic reversal of the magnetization for a given value of the field (infinite avalanche). Criticality is characterized by power-law distribution of avalanche sizes. Model predictions are contrasted with experimental results obtained in Cu–Al–Mn alloys.     

Phase Equilibrium and Critical Phenomena in the n-Pentan–Water and n-Hexane–Water Systems at High Temperatures and Pressures

Russian Physics Journal - PVTx-properties of the H2O – n-C5H12 and H2O – n-C6H14 mixtures are measured in the temperature range 303-680 K at pressures up to 60 MPa. The measurements...     

Critical number of solitons in the Bose–Einstein condensate

The dynamics of solitons in the Bose–Einstein condensate under the effect of the fluctuation interaction of condensate atoms is studied. A system of equations of motion describing changes in the parameters of the soliton wave function is obtained using the method of the averaged Lagrangian. The minimum critical number of solitons is found, and the influence of the fluctuation interaction on the dynamics of solitons near their critical width is studied.