Role of next-nearest-neighbour hopping in the internal structure of the ground state and finite temperature quantities of 2D t-J model

An exact diagonalization calculation for a small cluster in the two-dimensional t-J model has been studied to calculate two-hole correlation. Calculations reveal dominant hole-hole correlation for holes sitting on next-nearest-neighbour (NNN) sites and critical coupling occurs at J/t = 0.8. With the increase in negative-type NNN hopping, correlation decreases at NNN sites whereas it increases at other sites. The thermodynamic properties such as entropy and specific heat are studied as functions of temperature with various NNN hopping strength. Results show that with the inclusion of negative NNN hopping, the system becomes more ordered. A qualitative transition temperature region has been estimated. It is shown that with the increase in NNN hopping strength, T _c increases. Specific heat results show non-Fermi liquid-type behaviour of the system. All our calculations establish the importance of negative-type NNN hopping.     

Weak-coupling treatment of electronic (anti-)ferroelectricity in the extended Falicov-Kimball model

We study the (spinless) Falicov-Kimball model extended by a finite band width (hopping t _f ) of the localized (f-) electrons in infinite dimensions in the weak-coupling limit of a small local interband Coulomb correlation U for half filling. In the case of overlapping conduction- and f-bands different kinds of ordered solutions are possible, namely charge-density wave (CDW) order, electronic ferroelectricity (EFE) and electronic antiferroelectricity (EAFE). The order parameters are calculated as a function of the model parameters and of the temperature. There is a first-order phase transition from the CDW-phase to the EFE- or EAFE-phase. The total energy is calculated to determine the thermodynamically stable solution. The quantum phase diagrams are calculated.     

Frustration of antiferromagnetism in the t-t′-Hubbard model at weak coupling

The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t′. The asymptotic behavior of the critical coupling U_c(t′) at small t′ is calculated in dimensions d = 2,3, ∞ using Hartree theory; this yields the exact result at least in d > 2. The order of the transition is also determined. A region of stability of a metallic antiferromagnetic phase in d = 3 is identified.     

Kinetics of ordering in Ni1.50Sn (‘Ni3Sn2’) as revealed by the variation of the lattice parameters upon annealing

X-ray powder diffraction was employed to reveal the structural changes occurring upon annealing of quenched, hexagonal Ni_1.50Sn below its equilibrium ordering temperature, leading finally to long-range ordered, orthorhombic Ni_1.50Sn. The changes in the diffraction patterns indicate that the features of the low-temperature phase develop gradually in two main stages. Ex situ and in situ time-resolved X-ray powder diffraction analysis of the first stage was employed to monitor at various temperatures the time dependence of the lattice axial ratio c/a associated with the formation of long-range order in small domains. Data evaluation using an ‘equivalence-time’ method gave a value of 165–170?kJ/mol for the activation energy of the ordering, indicative of lattice-site changes of Ni atoms.     

Thermodynamic analysis of the quantum critical behavior of Ce-lattice compounds

A systematic analysis of low-temperature magnetic phase diagrams of Ce compounds is performed in order to recognize the thermodynamic conditions to be fulfilled by those systems to reach a quantum critical regime or, alternatively, to identify other kinds of low-temperature behavior. Based on specific heat (C _m ) and entropy results, three different types of phase diagrams are recognized: (i) with the entropy involved in the ordered phase (S _MO) decreasing proportionally to the ordering temperature (T _MO); (ii) those showing a transference of degrees of freedom from the ordered phase to a non-magnetic component, with their C _m (T _MO) jumps (ΔC _m ) vanishing at finite temperature; and (iii) those ending at a critical point at finite temperature because their ΔC _m do not decrease sufficiently with T _MO, producing an entropy accumulation at low temperature.

Only those systems belonging to the first case, i.e. with S _MO?→?0 as T _MO?→?0, can be regarded as candidates for quantum critical behavior. Their magnetic phase boundaries deviate from the classical negative curvature below T?≈?2.5?K, denouncing monotonic misleading extrapolations down to T?=?0. Different characteristic concentrations are recognized and analyzed for Ce-ligand alloyed systems. In particular, a pre-critical region is identified where the nature of the magnetic transition undergoes significant modifications, with its ?C _m /?T discontinuity strongly affected by the magnetic field and showing an increasing remnant entropy at T?→?0. Physical constraints arising from the third law at T?→?0 are discussed and recognized from experimental results.     

Effective interactions and superconductivity in the t-J model in the large-N limit

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C_4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature T_c is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. T_c increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively. Received: 16 June 1998 / Accepted: 14 July 1998     

Specific heat behavior of high temperature superconductors in the pseudogap regime

We consider the competition between the one dimensionalization effect due to a magnetic field and the hopping parameters in quasi-one-dimensional conductors. Our study is based on a perturbative renormalization group method with three cut-off parameters, the bandwidth E₀, the 1D-2D crossover temperature T^*₁, which is related to the hopping process t₁, and the magnetic energy . We have found that the renormalized crossover temperatures T^*₁ and T^*₂, at which the respectively hopping processes t₁ and t₂ become coherent, are reduced compared to the bare values as the field is increased. We discuss the consequences of these renormalization effects on the temperature-field phase diagram of the organic conductors.Received: 5 March 2003, Published online: 23 July 2003PACS: 64.60.-i General studies of phase transitions - 75.30.Fv Spin-density waves - 72.15.Gd Galvanomagnetic and other magnetotransport effects - 74.70.Kn Organic superconductors     

Phase transitions in the generalized spin-one-half Falicov–Kimball model in two dimensions

The extrapolation of small-cluster exact-diagonalisation calculations and the Monte-Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U _ff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave (CDW) phase and the spin-density-wave (SDW) phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The critical temperature T _c for a transition from the low-temperature ordered phases to the high-temperature disordered phase is calculated numerically for various values of J and U _ff .     

First and second order ferromagnetic transition at in a 1D itinerant system

We consider a modified version of the one-dimensional Hubbard model, the t ₁ - t ₂ Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t₂ to t₁. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T =0, the second order transition is a quantum magnetic critical point. Received 21 July 1999     

Temporal correlations and persistence in the kinetic Ising model: the role of temperature

We study the statistical properties of the sum S _t = dt'σ _t', that is the difference of time spent positive or negative by the spin σ _t, located at a given site of a D-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of S_t and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ( T > T _c), criticality ( T = T _c), and low temperature ( T < T _c). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents (x), in the low temperature phase. The probability that the temporal mean S _t/t was always larger than the equilibrium magnetization is found to decay as t ^{- - ?}. This yields a numerical determination of the persistence exponent in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model. Received 4 December 2000     

Phase transitions in the Falicov–Kimball model away from half-filling

The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ _c , changes to a different ordered phase and at the temperature, that can be several times higher than τ _c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.     

Superconductivity with s and p symmetries in an extended Hubbard model with correlated hopping

We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping for spin up (down) which depends on the total occupation n_b of spin down (up) electrons on both sites involved. The hopping parameters are t _AA , t_AB and t_BB for n _b =0,1,2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for t _AB <t _AA =t _BB and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences. Received: 2 February 1998 / Accepted: 17 March 1998     

Axial distribution of plasma fluctuations,plasma parameters,deposition rate and grain size during copper deposition

Floating potential fluctuations, plasma parameters and deposition rate have been investigated as a function of axial distance during deposition of copper in direct current (DC) magnetron sputtering system. Fluctuations were analyzed using phase space, power spectra and amplitude bifurcation plots. It has been observed that the fluctuations are modified from chaotic to ordered state with increase in the axial distance from cathode. Plasma parameters such as electron density (n_e), electron temperature (T_e) and deposition rate (D_r) were measured and correlated with plasma fluctuations. It was found that more the deposition rate, greater the grain size, higher the electron density, higher the electron temperature and more chaotic the oscillations near the cathode. This observation could be helpful to the thin film technology industry to optimize the required film.     

Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

Series Analysis of a Kosterlitz-Thouless Transition: The 6-State Planar Potts Model

A new implementation of the Finite Lattice Method of series expansion is used to derive low temperature series for the 6-state planar Potts model. This is expected to have Kosterlitz-Thouless transitions between the ordered low-temperature phase and a massless phase, and between the massless phase and a high-temperature disordered phase. In an exploratory study, we have analysed series for the order parameter to order x ⁵⁹. These series have proved particularly difficult to analyse and when seeking to both locate the transition and confirm the form of the Kosterlitz-Thouless transition, considerable ambiguity is found. If however the form of the Kosterlitz-Thouless transition is assumed, then the series analysis consistently indicates that the lower transition occurs at x _L=0.4886(10). A more conservative analysis, which made no assumption about the nature of the transition, led to the estimate x _L=0.485(8).     

Commensurate-incommensurate transition in two-coupled chains of nearly half-filled electrons

We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t _⊥ and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfinement crossover in this phase. A minimum of the charge gap is observed for values of t _⊥ close to this crossover. At large t _⊥ the region of the commensurate phase is enhanced, compared to a single chain. At the metal-insulator transition the Luttinger parameter takes the universal value K _ρ ^* = 1, in agreement with previous results on special limits of this model. Received 31 July 2000     

Topological phase diagram of a Kitaev ladder

We investigate the topological properties of a Kitaev ladder, i.e., a system made of two Kitaev chains coupled together by transversal hopping and pairing term, t₁ and Δ₁, respectively. Using the Chern number invariant, we present the topological phase diagram of the system. It is shown that beyond a non-topological phase, the system exhibits a topological phase either with four or two Majorana (zero energy) modes. In particular, we find that for some critical values of the transversal hopping t₁, and at a given transversal paring Δ₁, the topological phase survives also when the Kitaev criterion for the single chain (Δ > 0,   |μ| < 2t) is violated. Using a tight-binding analysis for a finite-size system we numerically check the bulk-edge correspondence.     

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M_H ≅ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L_t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.     

Unusual vortex dynamics in the quantum-liquid phase of a-MoxSi1−x films

We find the unusual vortex dynamics in the low-temperature liquid phase of amorphous Mo_xSi_1−x films by measuring the fluctuating component of the flux-flow voltage δV(t) about the average voltage. For the thick film, in which the quantum vortex liquid (QVL) phase has been well-determined in the field-temperature plane, δV(t) originating from the vortex motion is clearly visible in the QVL phase, where the distribution of δV(t) is anomalously asymmetric, implying large velocity and/or number fluctuations of driven vortices. For the thin film, in which the QVL phase has not been determined from the static transport measurements, similar unusual vortex motion is observed in nearly the same reduced-temperature regime. We suggest that vortex dynamics in the low-temperature liquid phase of thick and thin films is dominated by common physical mechanisms related to quantum-fluctuation effects.     

Magnetic properties of RPdIn (R=Gd–Er) compounds

AC susceptibility and DC magnetization measurements were performed for the RPdIn (R=Gd–Er) compounds both in the paramagnetic and in the ordered state. In opposite to GdPdIn, which is a ferromagnet (T_c=102 K), the other samples show a complex ferrimagnetic behavior with the additional transition at T_t<T_c. In the high-temperature phase (for T_t<T<T_c), a ferromagnetic interaction dominates, while in the low-temperature phase (for T⩽T_t) antiferromagnetic interactions with the magnetocrystalline anisotropy, especially strong for TbPdIn, come into play. The ordering temperatures are T_c=70, 34, 25 and 12.3 K for Tb-, Dy-, Ho- and ErPdIn respectively, while transition temperatures are T_t=6, 14 and 6 K for Tb-, Dy- and HoPdIn respectively. TbPdIn reveals an additional transition at 27 K connected with the intermediate ferrimagnetic phase. The critical fields for the magnetization process of the low-temperature phase are high (52 and 150 kOe for TbPdIn and 32 kOe for DyPdIn at T=4.2 K) yet these values decrease remarkably with increasing temperature. Results of the study are compared with magnetic and neutron diffraction data hitherto available. We state that irreversibility of the zero-field cooled–field cooled magnetization is not connected with the spin-glass phase claimed elsewhere.