High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

The Kubo–Martin–Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and Verboven, proposed an analogue to the KMS condition for infinite classical mechanical systems and highlighted its relationship with the Kirkwood–Salzburg equations and with the Gibbs equilibrium measures. In this paper, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose–Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden–Thompson inequality, Bogoliubov inequality and semiclassical analysis.

Ferrimagnetism in the Mean-Field Approximation of the Mixed Spin-3/2 and Spin-5/2 Ising System

Using the Mean-field theory based on Bogoliubov inequality for the free energy, a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies is investigated. The free energy of a mixed spin Ising ferrimagnetic system from MF approximation of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and compensation points. In particular, we investigate the effect of a single-ion anisotropy on the magnetic properties including the compensation phenomenon, in order to clarify the characteristic behaviours in a series of molecular-based magnets . The phase diagram of the system is also discussed in the anisotropy dependence of transition temperature. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

Thermal Entanglement and Critical Behavior of Magnetic Properties on a Triangulated Kagomé Lattice

The equilibrium magnetic and entanglement properties in a spin-1/2 Ising-Heisenberg model on a triangulated Kagomé lattice are analyzed by means of the effective field for the Gibbs-Bogoliubov inequality. The calculation is reduced to decoupled individual (clusters) trimers due to the separable character of the Ising-type exchange interactions between the Heisenberg trimers. The concurrence in terms of the three qubit isotropic Heisenberg model in the effective Ising field in the absence of a magnetic field is non-zero. The magnetic and entanglement properties exhibit common (plateau, peak) features driven by a magnetic field and (antiferromagnetic) exchange interaction. The (quantum) entangled and non-entangled phases can be exploited as a useful tool for signalling the quantum phase transitions and crossovers at finite temperatures. The critical temperature of order-disorder coincides with the threshold temperature of thermal entanglement.

Mean-field Solution of the mixed spin-1 and spin-5/2Ising system with different single-ion anisotropies

The mixed-spin ferrimagnetic Ising system consists of two-dimensional sublattices A and B with spin values and respectively .By used the mean-field approximation MFA of Ising model to find magnetism( ).In order to determined the best stabile magnetism , Gibbs free energy employ a variational method based on the Bogoliubov inequality .The ground-state (Phase diagram) structure of our system can easily be determined at , we find six phases with different spins values depend on the effect of a single-ion anisotropies .these lead to determined the second , first orders transition ,and the tricritical points as well as the compensation phenomenon .

Thermodynamics and Structure of Liquid Metals from a New Consistent Optimized Random Phase Approximation

We study thermodynamics and structural properties of several liquid metals to assess the validity of the generalized non-local model potential (GNMP) of Li et al. [J. Phys. F16, 309 (1986)]. By using a new thermodynamically consistent version of the optimized random phase approx­ imation (ORPA), especially adapted to continuous reference potentials, we improve our previous results obtained within the variational approach based on the Gibbs -Bogoliubov inequality. Hinging on the unified and very accurate evaluation of structure factors and thermodynamic quantities provided by the ORPA, we find that the GNMP yields satisfactory results for the alkali metals. Those for the polyvalent metals, however, point to a substantial inadequacy of the GNMP for high valence systems.