Self consistent theory of fluctuations near D-dimensional superconducting phase transitions

Nonlinear fluctuation contributions in the vicinity of the transition temperature for D-dimensional superconductors (D = 0…3) are treated in self-consistent Hartree approximation to the Ginzburg-Landau free energy. The results concern specific heat, correlation length, and the effect of a magnetic field on the specific heat (for D = 2).     

A mean-field study on the thermo-magnetic properties of GdxCo1−x amorphous alloys (0.16⩽x⩽0.25)

We present a mean-field study on the thermo-magnetic properties of Gd_xCo_1−x amorphous alloys in the 0.16⩽x⩽0.25 composition range. A single set of exchange integrals and fixed values of the angular momenta of Gd and Co fairly describe the temperature dependence of magnetization. The magnetic specific heat and magnetic entropy show field and composition dependence. Both the specific heat anomaly and the saturated entropy, at the temperature of the magnetic phase transition, increase with increasing Co concentration. The two magnetic subnetworks and their cross-interactions contribute differently to the specific heat.     

Heat capacity and magnetic susceptibility of ReO3

The specific heat and magnetic susceptibility of the transition metal oxide ReO₃ have been measured. The specific heat results give a Debye temperature Θ_D = 460 ± 10 K and an electronic specific heat coefficient γ = 6.45 ± 0.07 cal/mole K² which are in good agreement with similar measurements on the cubic sodium tungsten bronzes. The magnetic susceptibility and the electronic contribution to the specific heat are within a few percent of the corresponding parameters calculated from the free electron model with one electron per unit cell. Our results show that ReO₃ behaves much like a simple metal. No experimental evidence for narrow d-band effects was observed.     

Dyson equation for transverse ising paramagnet

The behavior of a confined magnetized ideal boson gas is examined. The effects of the dimensionalities of the system and the confinement potential as well as the effects of the field strength on the Bose-Einstein condensation are analyzed. It is shown that a phase transition does not occur in strongly confined systems. For the weakly confined gas a connection with the results of the non-confined magnetized gas is made. A correspondence is established between our results and those of a free gas of different dimensionality. The density of states of a particle moving in a three-dimensional space and confined by a cylindrically symmetric potential is calculated and used to explain the correspondence. The thermodynamic properties of the 3D - 2d gas are worked out in detail.     

Magnetic field effects in the cooperative Jahn-Teller system TbVO4

Effects of a magnetic field on the behaviors of TbVO₄ which shows a cooperative Jahn-Teller phase transition have been investigated. The possibility that the system will return to the undistorted phase at low temperatures in a magnetic field is considered. We show that because of the weak coupling of the system to the magnetic field applied along the c-axis, the magnetic field required to see the transition of the crystal back to the undistorted phase is impractically high. Diluting the crystal with nonmagnetic ions is then a plausible approach in the study of this novel behavior of the system. We have also calculated the effects of a magnetic field applied in the basal plane and shown that the crystal would remain distorted for all temperatures except the cases when the field is applied along the crystallographic axes. Finally, we consider the effects of a magnetic field on the temperature behavior of the specific heat and show that the Schottky anomaly which occurs at a very low temperature (～1°K) will be shifted to a higher temperature by applying a magnetic field.     

Quantum phase transitions in the anisotropic three dimensional XY model

In this paper we study the quantum phase transition in a three-dimensional XY model with single-ion anisotropy D and spin S=1. The low D phase is studied using the self consistent harmonic approximation, and the large D phase using the bond operator formalism. We calculate the critical value of the anisotropy parameter where a transition occurs from the large-D phase to the Néel phase. We present the behavior of the energy gap, in the large-D phase, as a function of the temperature. In the large D region, a longitudinal magnetic field induces a phase transition from the singlet to the antiferromagnetic state, and then from the AFM one to the paramagnetic state.     

Quasi-one-dimensional quantum spin liquid in the Cu(C<Subscript>4</Subscript>H<Subscript>4</Subscript>N<Subscript>2</Subscript>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-onedimensional insulator Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic T–H (temperature-magnetic field) phase diagram of CuPzN that contains Landau–Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling that of heavy-fermion compounds.     

Pairwise entanglement and critical behavior of an anisotropic ferrimagnetic spin chain

We studied the quantum phase transition revealed to occur in the ferrimagnetic mixed-spin (S,s)=(1,1/2) chain with positive crystal-field anisotropy D under an external magnetic field by using concepts from quantum information theory such as pairwise entanglement and purity, incorporated into the density matrix renormalization group algorithm. In this system, a magnetization plateau appears at 1/3 of the saturation magnetization for all values of D except for a critical value Dc where it vanishes. We obtained this value Dc=1.11445±0.00065 within the thermodynamic limit as local minima of the pairwise entanglement and the purity. Moreover, using this procedure we were able to investigate the second-order (or continuous) character of the quantum phase transition.     

Phase transition in a linear chain of classical spins with a logarithmic nearest neighbour pair potential

We present the complete calculation of the partition function and correlation functions of a linear array of classical spins coupled by a nearest neighbour logarithmic pair potential. In the case of a ferromagnetic coupling there occurs a phase transition at T_c > 0. The critical exponents of the specific heat C and the magnetic susceptibility χ (in the absence of an external field) are shown to have the non-classical value α = 2 and classical value γ = 1 respectively. The underlying mathematical mechanism of the phase transition is the complete degeneracy of all the eigenvalues of the corresponding integral equation (Kac's mechanism). Below T_c the partition function becomes complex. For antiferromagnetic coupling the free energy is analytic in the whole temperature range and so no phase transition occurs in this case.     

Superconductivity and calorimetric studies of Pr1.85Ce0.15CuO4+δ under different annealing conditions

Polycrystalline samples of electron-doped Pr_1.85Ce_0.15CuO_4+δ have been prepared under different annealing conditions and investigated by means of X-ray-diffraction, oxygen content analysis, electrical resistivity, magnetic susceptibility and low temperature specific heat measurements. X-ray-diffraction patterns show that samples contain a single T′ phase. The superconducting transition temperatures T_cm taken with the onset of diamagnetism in magnetic-susceptibility measurements are 20 and 19.5 K for sample annealed in flowing Ar gas and in vacuum (∼10⁻³ torr), respectively. The data of the samples, which are annealed in flowing Ar gas, show clear evidence for an αT² term at zero magnetic field in superconducting electronic specific heat, and are consistent with d-wave superconductivity. However, this behavior is not observed in the other sample, which is annealed in vacuum. These results indicate that different heat treatments affect the oxygen content, homogeneity, superconducting transition temperature T_c, superconducting volume fraction, and the superconducting pairing symmetry of Pr_1.85Ce_0.15CuO_4+δ.     

Transition De Phase Metamagnetique Du Bromure Ferreux

In a magnetic field parallel to the magnetization axis of an antiferromagnetic Fe Br₂ single crystal, a caracteristic metamagnetic behaviour is observed. The transition from an antiferromagnetic phase to a paramagnetic phase is studied by help of magnetization measurements in a steady field (H < 60 kOe). The measurement precision has allowed a detailed study of the magnetization isotherms, caracteristic of a first order magnetization phase transition (T < T_c = 4, 7 K) and of a second order phase transition (T_c < T < T_N = 14, 2 K).We have observed an original phase diagram. In a certain temperature and field range, the ordered phase is stable on the high temperature side of the transition point. Some theoretical studies in an Ising model, or in the hypothesis of a strong magnetoelastic coupling forecast the existence of such a magnetic phase diagram.At present, we proceed to a theoretical study, in a molecular field approximation, of the magnetic phase diagram of compounds similar to Fe Br₂ where we take into account the relative values of parameters J₁, J₂ and D associated with ferromagnetic and antiferromagnetic interactions and crystalline anisotropy.     

Superconducting properties of LaOs2

For superconducting LaOs₂ of the pure C-15 phase we measured the low temperature specific heat, the upper critical field and the susceptibility in the normal state. From the specific heat results we confirm the transition temperature of the C-15 phase and derive several thermodynamic parameters of the normal and superconducting state like γ, θ_D, ΔC, Δ(0), and H_c(0). The results suggest that LaOs₂ is an extremely strong coupling superconductor like La₃In and La₃Tl.     

Bose–Einstein condensation of a relativistic Bose gas in a harmonic potential

Using semiclassical method, Bose–Einstein condensation (BEC) of a relativistic ideal Bose gas (RIBG) with and without antibosons in the three-dimensional (3D) harmonic potential is investigated. Analytical expressions for the BEC transition temperature, condensate fraction, specific heat and entropy of the system are obtained. Relativistic effects on the properties of the system are discussed and it is found that the relativistic effect decreases the transition temperature T_c but enlarges the gap of specific heat at T_c. We also study the influence of antibosons on a RIBG. Comparing with the system without antibosons, the system with antibosons has a higher transition temperature and a lower Helmholtz free energy. It implies that the system with antibosons is more stable.     

Schwinger-boson mean-field theory of an anisotropic ferrimagnetic spin chain

By using the Schwinger-boson mean-field theory, the Heisenberg ferrimagnetic spin chain with the single-ion anisotropy D is explored. Based on the effect of the single-ion anisotropy D, we obtain four branches of the low-lying excitation and calculate the anisotropy dependence of spin reduction and the longitudinal correlation at zero temperature. We also discuss the free energy, magnetic susceptibility and specific heat at finite temperature with different anisotropy D.     

Magnetic properties of the mixed spin-5/2 and spin-3/2 Blume-Capel Ising system on the two-fold Cayley tree

We use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ₁ and Δ₂ are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D _A = Δ₁/J,D _B = Δ₂/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D _A or D _B increases. The first-order transitions only exist for some appropriate non-zero values of D _A and/or D _B . The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β ₀ of the model is estimated and found to be ¼ at small values of D _A = D _B = D and β ₀ = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.     

Specific heat and magnetic susceptibility of MnF2 and Mn0.98Fe0.02F2 near TN

The antiferro- to paramagnetic phase transition of the weakly anisotropic compound MnF₂ has been studied by means of heat capacity, magnetic susceptibility and thermal expansion measurements. The critical-point parameters associated with the specific heat indicate a transition according to the theoretical Ising-model. The temperature derivative of the parallel magnetic susceptibility times temperature (d(χ∥T)/dT) and the c-axis thermal expansion coefficient show a critical behaviour very similar to that of the specific heat. The influence of iron doping on the critical behaviour has been investigated by studies on Mn_0.98Fe_0.02F₂. Specific heat and magnetic susceptibility measurements show an unexpectedly sharp transition although some rounding off is noticed as compared to pure MnF₂.     

Island formation and condensation of a chemisorbed overlayer

The condensation of a chemisorbed overlayer from a lattice gas into a particular ordered structure in discussed in terms of the lattice-gas theory of Lee and Yang. The formation of islands of ordered structure is identified with the condensation phenomenon predicted by the theory. The phase diagram (transition temperature versus coverage) based on the theory of a two-dimensional Ising ferromagnet in zero magnetic field is constructed for the condensation of a lattice gas system with net attractive interactions between the particles. It is demonstrated that critical points at coverages other than θ = 0.5 are achieved for overlayer systems with unit meshes larger than (1 × 1). Low-energy electron diffraction results of the thermal disordering (island dissolution) for oxygen chemisorbed on W(110) are compared with the theory, and the effect of substrate surface heterogeneity on the phase diagram is discussed.     

Quantum Phase Transition and Thermal Entanglement in the Ising Model with Dzyaloshinskii-Moriya Interaction in an Inhomogeneous Magnetic Field

We investigate the quantum phase transition (QPT) and thermal entanglement in the two-qubit Ising model in an inhomogeneous magnetic field, and the DM interaction between the two lattices is considered. The results show the QPT highly relates to the magnetic intensity B and DM parameter D, by controlling the DM interaction D and external magnetic B we can change the positions of QPT points and the level spacing. Moreover, the QPT is closely related to thermal entanglement, when the QPT happens the ground state always changes between entanglement state and disentanglement state. The thermal entanglement highly depends on the system’s temperature T, DM intensity D and external magnetic field B. When T is lower, the entanglement can exhibit a platform-like region. By modulating the parameters D and B, the entanglement can be controlled and the entanglement switch can be realized.     

Quantum phase transition in lattice model of unconventional superconductors

In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature (T). Finite-T counterpart of the present model was proposed previously with which SC phase transition at finite T was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.     

Thermodynamics of the neutral Hubbard model

By use of Bogoljubov's variational principle the free energy of the neutral Hubbard model is calculated as a function of the total spinS _z . A transition from an antiferro-magnetic to a paramagnetic phase is found for all values of the coupling constantV ₀. The calculations are performed for the simple cubic and the body-centred cubic lattice; some numerical results are given for the transition temperature, the free energy, the sublattice magnetization, the transversal magnetic susceptibility and the response to a finite magnetic field.