Replica field theory and renormalization group for the Ising spin glass in an external magnetic field

We use the generic replica symmetric cubic field theory to study the transition of short-range Ising spin glasses in a magnetic field around the upper critical dimension. A novel fixed point is found from the application of the renormalization group. In the spin-glass limit, this fixed point governs the critical behavior of a class of systems characterized by a single cubic parameter. For this universality class, the spin-glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, however, behaves unusually. The physical consequences of this unusual behavior are discussed, and a comparison with the conventional de Almeida-Thouless scenario is presented.     

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     

Metastability region in spin-glasses

The stability of the Sherrington-Kirkpatrick model is reconsidered, pointing out that the de Almeida-Thouless line from the phase diagram does not imply the replica symmetry breaking at the zero magnetic field.     

Replica symmetry breaking for the Ising spin glass within cluster approximations

Within a class of cluster approximations, the Ising spin glass model on a d-dimensional hypercubic lattice is solved near the spin glass transition temperature. Spin glass order parameter function and Almeida-Thouless line are obtained.     

The sphericalp-spin interaction spin glass model: the statics

The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step replica symmetry breaking. The transition from the replica symmetric solution to the replica replica symmetry broken one is either continuous or discontinuous inq ₁–q₀ depending on the strength of the external magnetic field. The model can be solved explicitly for anyp at any temperature and magnetic field. Below the transition we find an infinite number of metastable states.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Quantum HeisenbergS=1/2 spin glass with ferromagnetic coupling and random Dzyaloshinskii-Moriya interactions

By means of the generalized static replica symmetric spin glass theory, a quantum HeisenbergS=1/2 spin glass model with the infinite-ranged random Dzyaloshinskii-Moriya (DM) interaction and ferromagnetic coupling is investigated. The dependence of entropy, specific heat, susceptibility and the corresponding order parameters on temperature is studied numerically for different ferromagnetic interactions and fixed anisotropy. Two spin glass phases has been found including transverse and mixed spin glass phases. It has been shown that the local susceptibility exhibits double-cusp features for different ferromagnetic coupling (J ₀). Phase transition poins are found in the specific heat-temperature plane at various ferromagnetic coupling values. Additionally, the dependence of the spontaneous moment on temperature is calculated.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Effective exponents for de almeida-thouless line

The experimental irreversibility line at the magnetic phase diagram H-T of spin glasses is often approximated using a power law Hα (T_G-T)^φ/2. The mean field theory of de Almeida and Thouless predicts φ=3 for temperatures T close to the spin-glass transition temperature T_G . For a range of reduced temperature involved in an experiment one should use, however, effective exponents (φ>3) obtained by fitting the power law to the exact expression for de Almeida-Thouless line. These compare favorably with experimental values of φ obtained for different spin glasses. The increase of effective exponent up to φ=7 on approaching the spin-glass-ferromagnetism multicritical point is also considered.     

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     

Replica symmetry breaking in and around six dimensions

Two, replica symmetry breaking specific, quantities of the Ising spin glass — the breakpoint x₁ of the order parameter function and the Almeida-Thouless line — are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results confirm that replica symmetry breaking does exist below d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x₁ has a nonzero and universal value for d<6 at criticality. Near six dimensions we have x1c=3(6−d)+O[²(6−d)]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.     

Quantum XY spin glass model with planar Dzyaloshinskii-Moriya interactions in longitudinal field

In the replica symmetric approximation and static limit in Matsubara “imaginary time”, the quantum XY spin glass model with planar Dzyaloshinskii-Moriya interaction in longitudinal field is investigated. Several thermodynamic quantities are calculated numerically as well as spin self-interaction and spin glass order parameter for spin S=1/2. It is shown that the entropy is not independent of the field. A crossover behavior of the specific heat depending on temperature is found. There is a deviation from the parabolic approximation, C/T=A+Bh ² . Received 11 March 1998     

Frustrated Blume-Emery-Griffiths model

A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean . Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with respect to fluctuations in replica space is analysed, and the transition lines are obtained both analytically and numerically. Received 13 January 1997     

Dynamic fracture model for acoustic emission

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x) is computed at high orders in powers of τ = T _c - T and H. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field. Received 3 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: andrea.crisanti@phys.uniroma1.it RID="b" ID="b"e-mail: tommaso.rizzo@phys.uniroma1.it RID="c" ID="c"e-mail: temtam@helios.elte.hu     

Exchange bias effect in partially oxidized amorphous Fe-Ni-B based metallic glass nanostructures

The magnetic properties of amorphous Fe-Ni-B based metallic glass nanostructures were investigated. The nanostructures underwent a spin-glass transition at temperatures below 100 K and revealed an irreversible temperature following the linear de Almeida-Thouless dependence. When the nanostructures were cooled below 25 K in a magnetic field, they exhibited an exchange bias effect with enhanced coercivity. The observed onset of exchange bias is associated with the coexistence of the spin-glass phase along with the appearance of another spin-glass phase formed by oxidation of the structurally disordered surface layer, displaying a distinct training effect and cooling field dependence. The latter showed a maximum in exchange bias field and coercivity, which is probably due to competing multiple equivalent spin configurations at the boundary between the two spin-glass phases.     

Tempering simulations in the four dimensional ±J Ising spin glass in a magnetic field

We study the four dimensional (4D) ±J Ising spin glass in a magnetic field with the simulated tempering algorithm recently introduced by Marinari and Parisi. We compute numerically the order parameter function P(q) and analyze the temperature dependence of the first four cumulants of the distribution. We discuss the evidence in favor of the existence of a phase transition in a field. Assuming a well defined transition we are able to bound its critical temperature.     

Spin glass ordering of Zn0.75Co0.25Fe0.5Cr1.5O4 cubic spinel

The linear and nonlinear low field AC susceptibilities of Zn_0.75Co_0.25Fe_0.5Cr_1.5O₄ show peaks due to non-critical contributions, which mask the peak due to spin glass ordering. They extend into the region of temperatures in which Mössbauer spectra do not show any magnetic component. When a DC field of 200 Oe suppresses the non-critical contributions, peak due to spin glass ordering is clearly visible. The spin glass ordering is thus shown to be a thermodynamic transition. The critical exponent is found to fall within the range found using other spin glasses. Mössbauer spectra in zero fields provide T_SG, which agrees with the peak temperature of AC susceptibilities in the absence of non-critical contributions. 〈S_Z〉 determined using Mössbauer spectra does not show any anomaly. In the presence of a field of 5 T, the spectra show SG ordering at 4.2 K, which converts into ferrimagnetic ordering at higher temperatures.     

Classical Heisenberg antiferromagnets with nearest and next-nearest neighbor interactions on the face-centered cubic lattice: a model for EuTe?

Magnetic properties of the Heisenberg antiferromagnet with spin quantum numberS on the face-centered cubic lattice are studied as function of temperature and magnetic field, using molecular field approximation and Monte Carlo methods. In order to model Europiumtelluride, we use isotropic exchange interactions between nearest- and nextnearest neighbors; the values of these exchange constants are taken from experiments. In addition, a pseudo-dipolar anisotropy (truncated after the next-nearest neighbor distance) is included; the molecular field calculations also are performed with the full dipolar of real EuTe in two respects: the structure in zero magnetic field involves 8 sublattices in the model rather than only two; the bicritical point, above which in the temperatureT magnetic fieldH plane the spin flop phase appears, occurs atH=0 in the model rather than at nonzero field. Possible additional interactions responsible for these discrepancies are discussed. Applying finite size scaling techniques we give also a preliminary analysis of the critical behavior of the model.     

Magnetic properties of the charge ordered Nd0.75Na0.25MnO3

Nd_0.75Na_0.25MnO₃ polycrystalline ceramic is prepared via sol-gel process and its magnetic properties and electron spin resonance (ESR) spectra have been investigated experimentally. As the compound is cooled from room temperature, a charge-ordered state first develops below 170 K. A high magnetic field melts the charge ordered state and stabilizes a ferromagnetic (FM) state below 170 K. A field induced transition, analogous to a spin flip transition, is observed between 40 and 170 K. The critical temperature for spin flip increases with increasing temperature. Below 130 K, the compound tends to be intrinsically inhomogeneous, i.e. FM clusters and paramagnetic domains coexist in this system at least, which is confirmed by ESR measurements. When the external magnetic field is zero, long range FM interaction is not developed in this system; however, a tendency of re-entrant FM transition is observed in this compound.