Ginzburg-Landau Expansion and the Upper Critical Field in the Disordered Attractive Hubbard Model (Brief Review)

We present a brief review of our studies of disorder influence upon Ginzburg-Landau expansion coefficients in Anderson-Hubbard model with attraction in the framework of the generalized DMFT + Σ approximation. A wide range of attractive potentials U is considered from weak coupling limit, where superconductivity is described by BCS model, to the limit of very strong coupling, where superconducting transition is related to the Bose-Einstein condensation of compact Cooper pairs, which are formed at temperatures significantly higher than the superconducting transition temperature, as well as the wide range of disorders from weak to strong, when the system is in the vicinity of Anderson transition. For the same range of parameters we study in detail the temperature behavior of orbital and paramagnetic upper critical field H_c2(T), which demonstrates the anomalies due both to the growth of attractive potential and to the effects of strong disordering.

     

Nonlinear Temperature Dependence of Magnetization of Two-Band Superconductors Near Upper Critical Field

Temperature dependence of the magnetization M （T） of two-band superconductors is studied in the vicinity of upper critical field He2 by using a two-band Ginzburg-Landau （GL） theory. It is shown that magnetization M（T） has a nonlinear character due to positive curvature of upper critical field Hc2（T） and temperature dependence of effective Ginzburg-Landau parameter Neff（T）. The results are shown to be in qualitative agreement with experimental data for the superconducting magnesium diboride, MgB2.     

The External Field Dependence of the BCS Critical Temperature

We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg–Landau equation.     

Upper Bounds on the Critical Temperature of the Ashkin-Teller Model

Starting from correlation identities for the Ashkin-Teller model and using correlation inequalities, we obtain rigorous upper bounds on the critical temperatures. The results were obtained in hexagonal, square, and cubic lattices and improve over effective field type calculations. The rigorous upper bounds results are compared to those obtained by other methods.     

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

We study Bose–Einstein Condensation (BEC) in the Infinite-Range-Hopping Bose–Hubbard model with repulsive on-site particle interaction in the presence of an ergodic random single-site external potential with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. We observe new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at certain fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the suppression of BEC at integer densities observed in Bru and Dorlas (J. Stat. Phys. 113:177–195, 2003) in the absence of a random potential, can disappear as the disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of the density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.     

Some Upper Bounds for the Critical Temperature for Ising Model with Four-spin Interactions

Upper bounds for the critical temperature of Ising models with different types of four-spin interactions on honeycomb and square lattices, which act only between the nearest-neighbor sites or to the nearest- and next-nearest-neighbor sites in addition to the conventional pair interactions, are obtained, using an exact relation for the two-spin correlation functions and rigorous inequalities for the spin correlation functions.     

The Critical Properties of One—Dimensional Extended Hubbard Model

In the framework of nonperturbative quantum field theory,the critical phenomena of one-dimensional extended Hubbard model (EHM) at half-filling are discussed from weak to intermediate interactions.After the EHM being mapped into two decoupled sine-Gordon models,the ground state phase diagram of the system is derived in an explicit way.It is confirmed that the coexisting phases appear in different interaction regimes which cannot be found by conventional theoretical methods.The diagram shows that there are seven different phase regions in the ground state,which seems not to be the same as previous discussions,especially the boundary between the phase separation and condensed phase regions.The phase transition properties of the model between various phase regions are studied in detail.     

Percolation Model of the Temperature Dependence of Exotic Magnetic Field in Doped Manganese Perovskites

We investigate the magnetic transitions in a （La1-x）2/3Ca1/3MnO3 system, which consists of paramagnetic and ferromagnetic domains, based on a magnetic theoretical percolation model In the mean-field approximation, the resistance as a function of temperature and magnetic field has been derived analytically and simulated numerically. It is found that the dependence of the critical temperature on magnetic field is linear when applied magnetic field is not too strong. Our theoretical predications are in good agreement with recent experimental observations.     

Magnetization Curve for One-Dimensional Hubbard Model in Critical Region

A power series expression of the exact solution of the one-dimensional (1D) Hubbard model in an external magnetic field is derived to study the an tiferromagnet-ferromagnet transition in the critical region. Aside from the magnetization curve, the critical field and susceptibility are analytically evaluated, and the results of these quantities in some limiting cases are discussed.     

Negativity in the Extended Hubbard Model under External Magnetic Field

We exactly calculate the negativity, a measurement of entanglement, in the two-site extended Hubbard model with external magnetic field. Its behaviour at different temperatures is presented. The negativity reduces with the increasing temperature or with the increasing uniform external magnetic field. It is also found that a non-uniform external magnetic field can be used to modulate or to increase the negativity.     

MgB2颗粒超导体临界电流的温度特性研究

通过制备MgB2/MgO超导复合材料,获得了典型的MgB2弱连接颗粒超导体,并测量了该样品在不同温度下的Ⅰ-Ⅴ特性曲线.在Ⅰ-Ⅴ曲线中,我们发现:当电流超过临界电流时,电压随着电流先是缓慢的增长,在电流升到一定值时,电压有一个很陡的突变.我们对这一变化进行了研究,认为这是由于MgO杂质使MgB2的晶界效应增强所引起的.该样品的临界电流和温度的关系满足:jc(T)∝(1-T/Tc)1/3,利用三维Josephson结网络系统的渗流模型进行计算发现,当颗粒超导系统处于非均匀状态时,临界电流和温度满足关系式jc(T)∝(1-T/Tc)4/3,这一结果和我们的实验符合的非常好.     

Geometric Upper Critical Dimensions of the Ising Model

The upper critical dimension of the Ising model is known to be dc = 4, above which critical behavior is regarded to be trivial. We hereby argue from extensive simulations that, in the random-cluster representation,the Ising model simultaneously exhibits two upper critical dimensions at(d_c = 4, d_p = 6), and critical clusters for d ≥ d_p, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric propertie...     

Finite Temperature Phase Diagram in the Half-Filled Extended Hubbard Model1

The CDW-SDW transition in the half-filled extended Hubbard model is investigated with the broken-symmetry Hartree theory formulated in terms of the Bogoliubov variational approach. The finite temperature phase-diagram in the weak coupling regime is derived analytically with a model density of states. The results show that there exist charge-order and antiferromagnetic order, but no mixed phase exists at any temperatures.     

Upper Bounds on the Critical Temperature for Kac Potentials

We consider an Ising system in two dimensions with a two body ferromagnetic interaction J _γ(x, y) that depends on the Kac scaling parameter γ. We prove that the inverse critical temperature β_cr(γ) is strictly above the mean-field value (equal to 1), namely that there exists C>0 so that for any b<C, β_cr(γ)> 1 + bγ²log γ^?1 for all γ sufficiently small. The temperature shift Cγ²log γ^?1 is to leading orders equal to the covariance of the magnetization fluctuations.     

Dependence of the Critical Temperature of Cylindrical Superconductors on the Boundary Conditions

Physics of the Solid State - The properties of long cylindrical superconductors with a diameter comparable with coherence length ξ have been investigated in the framework of the...     

The Upper Critical Dimension of the Abelian Sandpile Model

The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence of spanning subtrees of two-component spanning trees. Using equivalence between chemical paths on the spanning tree and loop-erased random walks, we reduce the problem to determination of the fractal dimension of spanning subtrees. Then the upper critical dimension d _u=4 follows from Lawler's theorems for intersection probabilities of random walks and loop-erased random walks.     

Perpendicular Upper Critical Magnetic Field in a Layered d-Wave Superconductor

JETP Letters - There exist numerous experimental studies of the perpendicular and parallel upper critical magnetic fields in $$d$$ -wave layered superconductors. They are usually theoretically...