Mean-field Transition Research Articles

Spin dynamics of aJ1−J2antiferromagnet and its implications for iron pnictides

Motivated by the recent observation of antiferromagnetic correlations in the paramagnetic phase of iron pnictides, we study the finite-temperature spin dynamics of a two-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnet. We consider the paramagnetic phase in the regime of a $(\ensuremath{\pi},0)$ collinear ground state, using the modified spin wave theory. Below the mean-field Ising transition temperature, we identify short-range anisotropic antiferromagnetic correlations. We show that the dynamical structure factor $\mathcal{S}(\mathbf{q},\ensuremath{\omega})$ contains elliptic features in the momentum space, and determine its variation with temperature and energy. Implications for the spin-dynamical experiments in the iron pnictides are discussed.

Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density

We study chiral symmetry restoration with increasing temperature and density in gauge theories subject to mutually perpendicular electric and magnetic fields using holography. We determine the chiral symmetry breaking phase structure of the D3/D7 and D3/D5 systems in the temperature-density-electric field directions. A magnetic field may break the chiral symmetry and an additional electric field induces Ohm and Hall currents as well as restoring the chiral symmetry. At zero temperature the D3/D5 system displays a line of holographic BKT phase transitions in the density-electric field plane, while the D3/D7 system shows a mean-field phase transition. At intermediate temperatures, the transitions in the density-electric field plane are of first order at low density, transforming to second order at critical points as density rises. At high temperature the transition is only ever first order.

Synchronization in interdependent networks

We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength JI) is ferromagnetically intercoupled (the strength J) to the Watts-Strogatz (WS) small-world network (the intranetwork coupling strength JII). In the absence of the internetwork coupling (J=0), the former network is well known not to exhibit the synchronized phase at any finite coupling strength, whereas the latter displays the mean-field transition. Through an analytic approach based on the mean-field approximation, it is found that for the weakly coupled 1D network (JI≪1) the increase of J suppresses synchrony, because the nonsynchronized 1D network becomes a heavier burden for the synchronization process of the WS network. As the coupling in the 1D network becomes stronger, it is revealed by the renormalization group (RG) argument that the synchronization is enhanced as JI is increased, implying that the more enhanced partial synchronization in the 1D network makes the burden lighter. Extensive numerical simulations confirm these expected behaviors, while exhibiting a reentrant behavior in the intermediate range of JI. The nonmonotonic change of the critical value of JII is also compared with the result from the numerical RG calculation.

Excitable Patterns in Active Nematics

We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic.

Fluctuations and critical temperature reduction in cuprate superconductors

We show theoretically that phase and amplitude fluctuations set in simultaneously in the cuprates. We then analyze fluctuations about ${T}_{c}$ in the specific heat of (Y,Ca)Ba${}_{2}$Cu${}_{3}$O${}_{7\ensuremath{-}\ensuremath{\delta}}$, YBa${}_{2}$Cu${}_{4}$O${}_{8}$, and Bi${}_{2}$Sr${}_{2}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$. The mean-field transition temperature, ${T}_{c}^{\mathrm{mf}}$, in the absence of fluctuations lies well above ${T}_{c}$ and at low doping reaches as high as 150 K. ${T}_{c}^{\mathrm{mf}}$ is found to be unrelated to the pseudogap temperature ${T}^{*}$, but scales with the gap ${\ensuremath{\Delta}}_{0}$, such that $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}^{\mathrm{mf}}$ is comparable to the BCS weak-coupling value 4.3, for $d$-wave superconductivity.

Magnetic transition and spin fluctuations in the unconventional antiferromagnetic compoundYb3Pt4

Muon spin rotation and relaxation measurements have been carried out on the unconventional antiferromagnetYb3Pt4. Oscillations areobserved below TN = 2.22(1) K, consistent with the antiferromagnetic (AFM) Néel temperature observed in bulkexperiments. In agreement with neutron diffraction experiments the oscillation frequencyωμ(T)/2π followsan S = 1/2 mean-field temperature dependence, yielding a quasistatic local field of 1.71(2) kOe atT = 0. A crude estimate gives an ordered moment of ∼ 0.66 μB atT = 0, comparableto 0.81 μB from neutron diffraction. As from above the dynamic relaxation rateλd exhibits no critical slowing down, consistent with a mean-field transition. In the AFM phase aT-linearfit to λd(T), appropriate to a Fermi liquid, yields highly enhanced values ofλd/T and the Korringaconstant Kμ2T/λd, with Kμ the estimated muon Knight shift. A strong suppression ofλd by applied field is observed in the AFM phase. These properties are consistentwith the observed large Sommerfeld–Wilson and Kadowaki–Woods ratios inYb3Pt4 (although the data do not discriminate between Fermi-liquidand non-Fermi-liquid states), and suggest strong enhancement ofq≈0 spin correlations between large-Fermi-volume band quasiparticles in the AFM phase ofYb3Pt4.

Magneto-transport studies of FeSe0.9 − xMx (M = Si, Sb)

We report on the magneto-resistivity ofFeSe0.9 − xMx (M = Si, Sb, x = 0.05, 0.1) down to 2 K in the presence of magnetic fields up to 14 T. The superconducting transitionshows marginal differences for Sb-and Si-doped samples. Normal state resistivity showsmarked changes at intermediate temperatures around 100 K, signaling the presence of astructural transition. It also shows linear behavior with temperature, reminiscent of highTc ceramics. Superconducting parameters like critical fields and coherence lengths arequantified for all samples. The broadening of superconducting transitions is studiedthrough thermally activated flux flow (TAFF) and fluctuation conductivity. The activationenergy of these superconductors is found to be one order smaller than the FeAs-1111system, which may be explained in terms of larger penetration depth. The activationenergy of thermally activated flux flow decreases with the Si and Sb doping and isexplained by Kramer’s scaling for grain boundary pinning. The zero-field andmagnetic-field-induced fluctuation conductivity are studied using Aslamazov–Larkin (AL)and lowest Landau level (LLL) theories, respectively. Zero-field fluctuation conductivityshows the 2D to 3D crossover just above the mean-field transition and 3D LLL scaling isobtained near mean-field transitions for magnetic-field-induced fluctuation conductivity.This is a clear indication of the three-dimensional nature of these superconductors. The 3Dnature of these superconductors signifies its potential for future technological applications.

Mechanism of conduction in TTF and TMTSF organic conductors from a study of their vibrational spectra

The charge transfer complexes of organic donors TTF and TMTSF have been prepared and studied with infrared spectroscopy. The nature of transition has been studied by analyzing features of absorption. TTF-TCNQ was found to be a Peierls semiconductor and not metallic. This shows that the mean field transition temperature is operative in TTF-TCNQ. TMTSF-TCNQ and TMTSF-DDQ showed lesser band gap than that of TTF-TCNQ. TTF-DDQ and TTF-I2 also showed very small band gap and were more conducting than TTF-TCNQ. The band gaps could be assigned to either the Peierls gap or the pinning gap of charge density waves.

Mean-field quantum phase transition in graphene and in general gapless systems

We study the quantum critical properties of antiferromagnetism in graphene at T=0 within mean-field (MF) theory. The resulting exponents differ from the conventional MF exponents, describing finite temperature transitions. Motivated by this, we have developed the MF theory of general gapless phases with density of states rho(E) |E|^r, r>-1, with the interaction as control parameter. For r>2, the conventional MF exponents \'a la Landau are recovered, while for -1<r<2, the exponents vary significantly with r. The critical interaction is finite for r>0, therefore no weak-coupling solution exists in this range. This generalizes the results on quantum criticality of the gapless Kondo systems to bulk correlated phases.

Ideal mean-field transition in a modulated cold atom system

We show that an atomic system in a periodically modulated optical trap displays an ideal mean-field symmetry-breaking transition. The symmetry is broken with respect to time translation by the modulation period. We describe experimental observations and develop a full microscopic theory of the observed critical phenomena. The transition is explained as resulting from the interplay of the long-range interatomic interaction and nonequilibrium fluctuations in the strongly modulated system. The observations, including anomalous fluctuations in the symmetry broken phase, are fully described by the theory.

Non-centro-symmetric superconductorsLi2Pd3B andLi2(Pd0.8Pt0.2)3B: amplitude and phase fluctuation analysis of the experimental magnetizationdata

We report on magnetization data obtained as a function of temperature and magnetic field inLi2(Pd0.8Pt0.2)3B andLi2Pd3B non-centro-symmetric superconductors. Reversible magnetization curves were plotted asM1/2 versusT. This allows study of the asymptotic behavior of the averaged orderparameter amplitude (gap) near the superconducting transition. Results ofthe analysis show, as expected, a mean field superconducting transition forLi2Pd3B. By contrast, a large deviation from the mean field behavior is revealed forLi2(Pd0.8Pt0.2)3B. This is interpreted as due to the strength of the non-s-wave spin-tripletpairing in this Pt-containing compound which produces nodes in the orderparameter and, consequently, phase fluctuations. The diamagnetic signal aboveTc(H) inLi2Pd3B is wellexplained by superconducting Gaussian fluctuations and agrees with the observed mean field transition. ForLi2(Pd0.8Pt0.2)3B the diamagneticsignal above Tc(H) is much higher than the expected Gaussian values and appears to be well explained bythree-dimensional critical fluctuations of the lowest-Landau-level type, which somehowagrees with the scenario of a phase mediated transition.

Fluctuation conductivity of single-crystalline BaFe1.8Co0.2As2 in the critical region

The magnetofluctuation conductivity, called excess conductivity, originated from the forming of the superconducting droplet near to the mean-field transition temperature, was measured for the optimally doped BaFe1.8Co0.2As2 single crystals with a critical temperature, Tc, of 24.6 K. This measurement of the excess conductivity for magnetic fields up to 9 T was compared with the thermodynamic scaling theory in the critical region, in which not only the Gaussian fluctuation but also fourth order terms of the order parameter are included. An analysis of the excess conductivity showed that the superconductivity followed three-dimensional scaling rather than two-dimensional scaling even though the sample had a layered structure.

Hysteresis loop signatures of phase transitions in a mean-field model of disordered Ising magnet

The multiplicity of long-lived states in frustrated disordered magnets makes the task to experimentally deter-mine which of them has the lowest free energy (and thus what thermodynamic phase the sample is in) seem rather hopeless. Nevertheless here we show in the framework of Landau-type phenomenological model that signatures of the mean-field equilibrium phase transitions in such highly nonequilibrium systems may be found in the evolution of the hysteresis loop form. Thus the sequence of transitions from spin-glass to mixed phase and to ferromagnetic one results in the changes from inclined hysteresis loop to that with the developing vertical sides and to one with the perfectly vertical sides. Such relation between loop form and the location of global minimum may hold beyond the mean-field approximation and can be useful in the real experiments and Monte-Carlo simulations of the problems involving rugged potential landscape.

Anomalous Transport and Possible Phase Transition in Palladium Nanojunctions

Many phenomena in condensed matter are thought to result from competition between different ordered phases. Palladium is a paramagnetic metal close to both ferromagnetism and superconductivity and is, therefore, a potentially interesting material to consider. Nanoscale structuring of matter can modify relevant physical energy scales, leading to effects such as locally modified magnetic interactions. We present transport measurements in electromigrated palladium break junction devices showing the emergence at low temperatures of anomalous sharp features in the differential conductance. These features appear symmetrically in applied bias and exhibit a temperature dependence of their characteristic voltages reminiscent of a mean-field phase transition. The systematic variation of these voltages with zero bias conductance, together with density functional theory calculations illustrating the relationship between the magnetization of Pd and atomic coordination, suggests that the features may result from the onset of spontaneous magnetization in the nanojunction electrodes. We propose that the characteristic conductance features are related to inelastic tunneling involving magnetic excitations.

Raman scattering evidence for a cascade evolution of the charge-density-wave collective amplitude mode

The two-dimensional rare-earth tritellurides undergo a unidirectional charge-density-wave (CDW) transition at high temperature and, for the heaviest members of the series, a bidirectional one at low temperature. Raman scattering experiments as a function of temperature on ${\text{DyTe}}_{3}$ and on ${\text{LaTe}}_{3}$ at 6 GPa provide a clear-cut evidence for the emergence of the respective collective CDW amplitude excitations. In the unidirectional CDW phase, we discover that the amplitude mode develops as a succession of two mean-field BCS-like transitions with different critical temperatures, which we associate with the presence of two adjacent Te planes in the structure.

Excitonic condensation in a double-layer graphene system

The possibility of excitonic condensation in a recently proposed electrically biased double-layer graphene system is studied theoretically. The main emphasis is put on obtaining a reliable analytical estimate for the transition temperature into the excitonic state. As in a double-layer graphene system the total number of fermionic ‘flavors’ is equal to N = 8 due to two projections of spin, two valleys and two layers, the large-N approximation appears to be especially suitable for theoretical investigation of the system. On the other hand, the large number of flavors makes screening of the bare Coulomb interactions very efficient, which, together with the suppression of backscattering in graphene, leads to an extremely low energy of the excitonic condensation. It is shown that the effect of screening on the excitonic pairing is just as strong in the excitonic state as it is in the normal state. As a result, the value of the excitonic gap Δ is found to be in full agreement with the previously obtained estimate for the mean-field transition temperature Tc, the maximum possible value Δmax, Tmaxc ∼ 10−7ϵF (ϵF is the Fermi energy) of both being in a 1mK range for a perfectly clean system. This proves that the energy scale ∼10−7ϵF really sets the upper bound for the transition temperature and invalidates the recently expressed conjecture about the high-temperature first-order transition into the excitonic state. These findings suggest that, unfortunately, the excitonic condensation in graphene double-layers can hardly be realized experimentally.

Quantum effects on criticality of an Ising model in scale-free networks: Beyond mean-field universality class

We study the effect of quantum fluctuations on the critical behavior of the Ising ferromagnetic phase transitions that do not belong to the mean-field universality class. A model system is considered, in which Ising spins are placed on the nodes of a scale-free network. Our Monte Carlo analysis shows that the critical exponents differ from those of mean-field phase transitions when degree exponent gamma is in the range 3<gamma<5 . This confirms earlier analytic calculations based on ansatzes and approximation methods. As we apply quantum fluctuations by means of a magnetic field perpendicular to the Ising spin direction, the transition temperature T(c) decreases with increasing magnetic field strength. We find, however, that the quantum fluctuations do not alter the critical exponents and the universality class remains unchanged.

Nonlocal quark model beyond mean field and QCD phase transition

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted to the physical values of the pion mass and the weak pion decay constant. The size of the 1/Nc correction to the quark condensate is carefully studied in the nonlocal and the usual local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. It is also found that the 1/Nc corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition point.

A model for dimensional crossover temperature above the superconducting transition for high-temperature superconductors

We have developed a theoretical model for the calculation of dimensional crossover temperature above the mean-field transition temperature using paraconductivity approach. We have numerically estimated the dimensional crossover (2D–3D and 2D–1D) temperature for the recently reported polycrystalline sample of the type Hg, Tl-1223. Our numerical results indicate that the dimensional crossover temperature is a variable quantity and it depends on the parameter related to superconductivity and the range of temperature where the fluctuation effect is significant.

On the anisotropy of lattice polymers

We quantified the anisotropy of various lattice models used in polymer simulations based on two quantities: the Fourier transform of the normalized Boltzmann factor of allowable bonds on a lattice (which is the central quantity for describing lattice chain conformations) and the bulk lamellar period at the mean-field order-disorder transition (ODT) of symmetric diblock copolymers on a lattice (which is pertinent to the study of microphase separation). This allowed us to compare the anisotropy of different lattices and to design new lattice models that minimize the quantified anisotropy. A lattice field theory based on the same Hamiltonian used in the newly proposed fast lattice Monte Carlo simulations [Q. Wang, Soft Matter 5, 4564 (2009)] is also presented, along with some mean-field results on the ODT of symmetric diblock copolymers on these lattices obtained under the random-phase approximation.