Scaling and infrared divergences in the replica field theory of the Ising spin glass

Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w². Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w² and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed. Received 23 December 1998 and Received in final form 23 March 1999     

Spin-ordering in S = 1 anisotropic Heisenberg models with nondiagonal spin exchange

The properties of S = 1 anisotropic Heisenberg models with nondiagonal exchange between axial and planar spin components are investigated using Monte Carlo techniques. The quantum nature is taken into account in a semi-classical approximation. The ordering of the spins when applying an external field with axial and planar components is discussed. It is argued that the quantum nature of the spins and the nondiagonal exchange may explain the peculiar shape of the magnetic specific heat of FeBr₂ as well as the weakly first-order phase transition observed in the same compound when a tilted field is applied. Received 24 January 1999     

Magnetic relaxation phenomena in a CuMn spin glass

Experiments on the temperature and time dependence of the response function and the field cooled magnetisation of a Cu(Mn) spin glass at temperatures below the zero field spin glass temperature are used to explore the non-equilibrium nature of the underlying spin configuration. The results imply that a certain spin configuration is imprinted on the system as the temperature is decreased at a constant cooling rate. The cooling rate governs the magnitude of the FC magnetisation ((H,T)). Any intermittent halt at a constant temperature, , imprints an extended spin configuration, a process that is reflected e.g. in a downward relaxation of . On continued cooling at the same rate, the magnitude of (T) remains at a lower level than that of a continuous cooling curve. These results are put into the context of the corresponding behaviour of the response function as observed in measurements of the relaxation of the zero field cooled magnetisation. Received 27 October 1998 and Received in final form 30 November 1998     

Sensitivity to temperature perturbations of the ageing states in a re-entrant ferromagnet

Dynamic magnetic properties and ageing phenomena of the re-entrant ferromagnet (Fe_0.20Ni_0.80)₇₅P₁₆B₆Al₃ are investigated by time dependent zero field cooled magnetic relaxation, m(t), measurements. The influence of a temperature cycling (perturbation), ,(prior the field application) on the relaxation rate is investigated both in the low temperature re-entrant spin glass “phase” and in the ferromagnetic phase. In the ferromagnetic phase the influence of a positive and a negative temperature cycle (of equal magnitude) on the response is almost the same (symmetric response). The result at lower temperatures, in the RSG “phase” is asymmetric, with a strongly affected response for positive, and hardly no influence on the response for negative temperature cycles. The behaviour at low temperatures is similar to what is observed in ordinary spin glasses. Received 20 August 1998     

Evidence of critical fluctuations from the magnetoconductivity data in Bi2Sr2Ca2Cu3O10+x phase

The fluctuation-induced magnetoconductivity of the Bi₂Sr₂Ca₂Cu₃O_10+x phase is studied above zero-field critical temperature Tc(0) and for moderate magnetic fields. It is found that the Gaussian approximation for superconducting fluctuations underestimates the negative fluctuation magnetoconductance drastically in the Tc(0) < T < Tc(0) + 20 K temperature range. Taking into account the critical fluctuation contribution on the base of self-consistent Hartree approximation makes it possible to explain the data quantitatively in terms of the only Aslamazov-Larkin contribution for different magnetic fields and temperatures, consistently with the zero field data. Received 14 April 2000 and Received in final form 13 July 2000     

Structure of spin polarons in the t-t′ -t″ -Jz model

We calculate the Green function in the t-t '-t ”-J^z model and analyze the deformation of the quantum Néel state in the presence of a moving hole. Solving the problem in a self-consistent Born approximation and using Reiter's wave function we have found various spin correlation functions. We show that the different sign of hopping elements between the hole- and electron-doped system of high- cuprates is responsible for the sharp difference of the polaron structure between the two systems with antiferromagnetism stabilized in the electron-doped case by carriers moving mainly on one sublattice. Received 11 January 2000     

On the T Bloch law in magnets with fourth-order exchange interaction

For the ferromagnets EuS and GdMg, in which fourth-order exchange interactions (i.e. biquadratic, three-spin and four-spin interactions) have been identified, the deviation of the spontaneous magnetization with respect to the T =0 value is shown to follow a T² law instead of the famous T3/2 law expected for a Heisenberg ferromagnet. Moreover, the observed T² law holds for temperatures as large as 0.8T_C and the extrapolated magnetization value for does not conform to ferromagnetic saturation. This is because the fourth-order exchange interactions generate a second order-parameter which is assumed to govern the order of the transverse moment components. These moment components have a finite expectation value for at the expense of the Heisenberg order parameter. Like the spontaneous magnetization, the critical field curves B c ( T ) of the metamagnet EuSe and the antiferromagnet EuTe also start decreasing with a T² term for . It is argued that the T² law is a consequence of the fourth-order exchange interactions. This is shown experimentally by a study of the critical field curves [0pt] pertinent to the longitudinal (Heisenberg) order-parameter in the diamagnetically diluted antiferromagnets Eu_xSr_1-xTe. In this solid solution series a particular composition of x c =0.85 exists at which the different fourth-order interaction processes compensate each other in the high temperature average. As a consequence, an Eu_xSr_1-xTe sample with x =0.85 meets the requirements of a Heisenberg antiferromagnet at least if a quantity is considered for which the high-temperature average over all fourth-order interactions is decisive. This seems to be the case for the critical field curve [0pt] which gives the phase boundary to the paramagnetic phase. In fact, a crossover from a T² to a T3/2 law is observed for [0pt] on approaching x_c. This, we believe, shows the frequently observed T² law is caused by the fourth-order interactions. Received 23 July 1998 and Received in final form 12 October 1998     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

The Kondo effect in periodic narrow-band systems

The Kondo divergences owing to interaction of current carriers with local moments in highly correlated electron systems are considered within the Hubbard and s-d exchange models with infinitely strong on-site interaction, the many-electron Hubbard representation being used. The picture of density of states containing a peak at the Fermi level is obtained. Various forms of the self-consistent approximation are used. The problem of the violation of analytical properties of the Green's function is discussed. Smearing of the “Kondo” peak owing to spin dynamics and finite temperatures is investigated. Received 25 November 1999 and Received in final form 31 January 2000     

Second- to first-order transition in two coupled antiferromagnetic rings

We numerically investigate an S=1/2 spin model, in which two dimerized antiferromagnetic rings interact with each other ferromagnetically. It is shown that the order of the magnetoelastic transition is strongly affected by the interring coupling J_⊥ and there may exist a critical J_⊥^* dividing the first-order transition and the continuous transition.     

The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to −∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.     

Random magnetic interactions and spin glass order competing with superconductivity: Interference of the quantum Parisi phase

We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for all temperatures T and chemical potentials μ. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are presented together with a few results for -step breaking. Suppression of reentrant SG-SC-SG transitions due to RPSB is found and discussed in context of ferromagnet-SG boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments in heavy fermion systems and high superconductors. We find a crossover line traversing the SG-phase with as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates a random field instability and suggest Dotsenko-Mézard vector replica symmetry breaking to occur at low temperatures beyond. Received 26 November 1998 and Received in final form 25 January 1999     

Electronic structure and properties of strontium ferrite Sr3Fe2O6

The electronic structure of strontium ferrite Sr₃Fe₂O₆ was calculated using the tight-binding linear muffin-tin orbital method (TB LMTO) in the local spin density approximation of density functional theory with Coulomb correlations correction (LSDA+U). The semiconducting character of the spectrum with charge transfer energy gap of 1.82 eV was obtained in reasonably good agreement with experimental data. The iron ions are found to be in the high spin state. The calculated value of the local spin magnetic moment of Fe³⁺ ion is 3.94 μ_B which is not typical for trivalent iron ion in the high spin state. It is shown that the strong hybridization between Fe3d and O2p orbitals favors the d⁶ L configuration of Fe³⁺ ion, where L is a hole in the oxygen p shell. The mechanism of oxygen transport in ferrite is discussed basing on the total energy calculations of the different spatial configurations of oxygen vacancies.     

Frequency-dependent fluctuational conductivity above in anisotropic superconductors: effects of a short wavelength cutoff

We discuss the excess conductivity at nonzero frequencies in a superconductor above T_c within the Gaussian approximation. We focus the attention on the temperature range not too close to T_c: within a time-dependent Ginzburg-Landau formulation, we phenomenologically introduce a short wavelength cutoff (of the order of the inverse coherence length) in the fluctuational spectrum to suppress high momentum modes. We treat the general cases of thin wires, anisotropic thin films and anisotropic bulk samples. We obtain in all cases explicit expressions for the finite frequency fluctuational conductivity. The dc case directly follows. Close to T_c the cutoff has no effect, and the known results for Gaussian fluctuations are recovered. Above T_c, and already for ε = ln(T/T _c) > 10^-2, we find strong suppression of the paraconductivity as compared to the Gaussian prediction, in particular in the real part of the paraconductivity. At high ε the cutoff effects are dominant. We discuss our results in comparison with data on high-T_c superconductors. Received 19 March 2002 Published online 25 June 2002     

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. Received 8 February 1999 and Received in final form 14 June 1999     

Power law distributions and dynamic behaviour of stock markets

A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t ^′ = 2Dδ t-t ^′ and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψϕ - ln G(ϕ)} where Ψϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ² - cϕ³ and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ≫ɛ, a distribution function with power law tails, viz: P ϕ = exp{2bϕ-cϕ² /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D≈ | J|. Received 25 July 2000     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998