Construction of phase diagrams for nanoscaled Ising thin films on the honeycomb lattice using cellular automata simulation approach

The phase diagrams of the three-layer Ising model on the honeycomb lattice with a diluted surface have been constructed using the probabilistic cellular automata based on Glauber algorithm. The effects of the exchange interactions on the phase diagrams have been investigated. A general mathematical expression for the critical temperature is obtained in terms of relative coupling r = J₁/J and Δ_s = (J_s/J) ? 1, where J and J_s represent the nearest neighbor coupling within inner- and surface-layers, respectively, and each magnetic site in the surface-layer is coupled with the nearest neighbor site in the inner-layer via the exchange coupling J₁. In the case of antiferromagnetic coupling between surface-layer and inner-layer, system reveals many interesting phenomena, such as the possibility of existence of compensation line before the critical temperature.     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

Phase transitions in the spinless Falicov-Kimball model with correlated hopping

The canonical Monte-Carlo is used to study the phase transitions from the low-temperature ordered phase to the high-temperature disordered phase in the two-dimensional half-filled Falicov-Kimball model with correlated hopping. As the low-temperature ordered phase we consider the chessboard phase, the axial striped phase and the segregated phase. It is shown specifically for weak coupling, which is the most interesting regime, that all three phases persist also at finite temperatures (up to the critical temperature τ _c ) and that the phase transition at the critical point is of the first order for the chessboard and axial striped phase and of the second order for the segregated phase. In addition, it is found that the critical temperature is reduced with the increasing amplitude of correlated hopping t' in the chessboard phase and it is strongly enhanced by t' in the axial striped and segregated phase.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J _z is different from the lateral one J _l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J _l ? J _z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.     

Finite size scaling for critical parameters of simple diatomic molecules

We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres, Z ⁺ e ^?Z⁺. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Z_c = 1.228279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.     

The thermoelastic behaviour of the orientationally disordered ionic crystals in two dimensions

The anomalous temperature dependence of the elastic constantsc ₁₁ andc ₆₆ and the elastic instability temperatureT _c are obtained in the two-dimensional microscopic model of the alkali cyanides crystals. It has been found, by means of the Michel and Naudts' theory of the translation rotation coupling, that the orientational disorder in the high-temperature phase leads to the critical softening of the shear elastic constantc ₆₆.     

Coupling of orientational and translational modes in solid C60 and C70

The orientational phase transitions in solid C₆₀ and C₇₀ are accompanied by quite different anomalies in the crystalline strains. In solid C₆₀ the phase transition Fm3m→Pa3 is primarily an orientational effect (antiferro-rotational), which is driven by the condensation of orientational modes belonging to X₅ ⁺ irreducible representation (irreps) of Fm3m. These modes are the primary order parameters (oops) and their number is equal to the number of irreps of T_2g and T_1g symmetry within the manifolds under consideration. Taking into account irreps up to the manifold 1=12, we have studied the rotation-rotation-translation (RRT) coupling between the oops and the lattice displacements. We have investigated the resulting lattice contraction and the change of the elastic constant c₁₁ at the phase transition. In solid C₇₀ (fcc-phase) we investigate the bilinear coupling of orientational fluctuations of T_2g symmetry to transverse acoustic lattice displacements. This coupling is the driving mechanism for the ferroelastic phase transition Fm3m → R3m. Finally we investigate the transition from the rhombohedral phase to a low temperature monoclinic phase. This transition in antiferro-rotational.     

Spin-orbit coupling in the superconducting phase and DDW states of high-T<Subscript>c</Subscript> cuprates

The effects of the spin-orbit coupling are considered for the high T _c cuprates with asymmetric superconducting gap (SC) and the d-density wave (DDW) phase due to its vital role in the experimental determination of the DDW state. Experiments predict an anisotropy in the DSC gap where |Δ(0,π)|>|Δ(π,0)| and the gap node deviates from the diagonal direction towards the k _x axis. Measurements also demonstrate DDW to be a possible candidate for the pseudogap in the underdoped phase. Due to the spin-orbit (SO) coupling in the low temperature orthorhombic (LTO) phase, the phase diagram of the cuprates suffers a change due to the modification of the T* value, the temperature characteristic of pseudogap, although T _c remains unaltered. Moreover, for a more generalized SO coupling, the DDW gap decreases with the angle but has no effect on the SC gap. We calculate the density of states in the various regimes of doping for the mixed SC+DDW states in the underdoped (UD) phase, SC state in the overdoped phase and also the DDW state in the UD phase and compare them with various theoretical and experimental works. The temperature dependence of the specific heat does not exhibit any qualitative change due to the SO coupling.     

Critical disorder effects in Josephson-coupled quasi-one-dimensional superconductors

Effects of non-magnetic randomness on the critical temperature T _c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T _c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T _c ⁽¹⁾ and T _c , which correspond to pair-breaking and phase-coherence breaking. The interplay between disorder and quantum phase fluctuations results in quantum critical behavior at T = 0, manifesting itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.     

Unconventional magnetic phase diagram of cuprate superconductor La2−xSrxCuO4 at quantum critical point x=1/9

We propose a new magnetic phase diagram of La_2?xSr_xCuO₄ around a quantum critical point x=1/9 based on field-cooled magnetization measurements and critical fittings. A new phase boundary T_m2(H) is discovered which buries deeply below the first order vortex melting line in the vortex solid phase. The coupling between superconductivity and antiferromagnetism is found to be attractive below T_m2(H) while repulsive above. The attractive coupling between superconducting order and static antiferromagnetic order provides compelling experimental evidence that the antiferromagnetism microscopically coexists and collaborates with the high temperature superconductivity in cuprates.     

Phase and frequency shifts of two nonlinearly coupled oscillators

We analyze two nonlinearly phase coupled oscillators with eigenfrequencies ω₁and ω₂, where n\gw₁=m\gw₂+\gp, with integern andm. For \gh=0 there are up to four stable synchronized states which differ from each other only by the difference of the oscillators\rs phases. The number of different synchronized states depends on the coupling constants. If \gh does not vanish phase shifts and frequency shifts may occur givig rise to stable synchronized states which also differ from each other due to the frequencies. By means of the center manifold theorem we calculate these shifts explicitely. Different coupling constants are investigated: symmetrical, homogenously asymmetrical and arbitrary coupling constants. Our results point out the decisive influence of the symmetry of the coupling constants upon the frequency and phase shifts. Moreover the local stability of the unperturbed synchronized state (i.e. for \gh=0) determines the magnitude of the frequency and phase shifts.     

Critical temperature of low-dimensional high-T c superconductors

We generalized the Coherent Potential Approximation (CPA) method for the calculation of the critical temperature of superconductors of lower dimensionality. Two dimensional (2d) and one-dimensional (1d) models have been considered. The critical temperature is calculated as function of the electronic concentration and of the position of the Fermi level. The critical temperature can be expressed with either of these two parameters. We also calculate the dependence ofT _c on an additional parameter which is the measure of the interplane coupling.     

三重态双极化子的超导A相与B相

本文应用对称破缺的自洽Hartree近似讨论了三重态双极化子的超导A相和B相。在弱耦合的情况下,通过自由能的计算得到B相总比A相稳定;在强耦合的情况下,加入涨落反馈项可使得A相的自由能比B相的自由能低,或者发生A相到B相的转变,这和³He超流的情形类似。本文还精确计算了超导稳定相的热力学临界场H_c随温度的变化,并与重费密子超导体UBe₁₃,UPt₃和URi₂Si₂的上临界场作了比较,发现H_c能定性解释所有这些超导体的上临界场的反常温度特性。 关键词：     

Magnetoelastic instability in the XXZ rings with next-nearest neighbour coupling

This paper numerically investigates the magnetoelastic instability in the S = 1/2 {XXZ} rings containing finite spins N with antiferromagnetic nearest-neighbour ({NN}) and next-nearest neighbour ({NNN}) coupling. It finds that, as the {NN} anisotropy Δ₁ equals the {NNN} anisotropy \varDelta₂, there exists a critical {NNN} coupling strength J₂^c(≈0.5), at which the systems always locate in dimerized phase for arbitrary large spring constant. As Δ₁ \ne Δ₂, the values of J₂^{\rm c} are dependent on N and the difference of (Δ₁-\varDelta₂).     

Nucleon Properties Below the Critical Point Temperature

In this paper, we extended our work (Abu-Shady, Int. J. Theory Phys. 49:2425, 2010) to include nucleon properties. The field equations have been solved in the mean-field approximation using the effective mesonic potential at finite temperature. We found that the nucleon first mass increases up to \frac45 T_c\frac{4}{5} T_{c} MeV (where T _c is the critical point temperature) then decreases at higher values of temperature which approach the critical temperature (T _c ). In addition, we found that the magnetic moments of the proton and neutron can be increased by increasing the temperature up to the critical temperature. Moreover, we examined the axial coupling constant g _A (0), and the pion-nucleon coupling constant g _πNN (0) as functions of temperature. The obtained results are compared with previous works. From the results, we conclude that finite temperature plays a significant role in the change of behavior of nucleon properties.     

Ground state properties of the falicov-kimball model in the strong coupling limit

We present some analytic results concerning the ground state of the one-dimensional Falicov-Kimball model in the strong coupling limit. Using the perturbation theory, we find: (i) The well-expected phase segregation takes place for ¦U¦ (U is the interaction strength), (ii) For finiteU there exists the critical value of the interaction strengthU =U _c, below which the segregated phase — an incoherent mixture of the empty and full lattices cannot be the ground state of the model. We give the analytical expression for this boundary. Finally, we discuss the phase diagram of the model for some special configuration of ions.     

Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δ_cr = 0.251 for U = ∞ and a critical coupling of U_cr = 77.7t. Both values improve previous variational results considerably.     

A mode coupling analysis of the central peak at order disorder phase transitions

The influence of local and translation invariant memory effects on the critical dynamics of a model undergoing a continous structural phase transition from a disordered (T>T _c ) to an ordered distorted phase (T>T _c ) is studied by mode coupling theory above the critical temperatureT _c . It is shown that besides the existence of critical slowing-down modes there also exists a central peak as a consequence of correlations of the critical modes, increasing with the critical exponent when approachingT _c . The dependence of the central peak on the wavevector , temperatureT and on the spatial dimensiond is investigated. Ford=3 a scenario withlocal long time memory correlations is compared with respect to its temperature and momentum dependence with a model using translation invariant long time memory correlations.