Reentrant behaviour in spin glasses

We present the phase diagram of thed-dimensional random bond Ising model as a representative system for spin glasses. We consider nearest neighbour ferromagnetic couplingsJ with concentration 1-p and impurity couplingsaJ (|a|1) with concentrationp. It is shown that for antiferromagnetic couplings, –1<a<0, the system quite generally exhibits reentrant behaviour, i.e. two phase transitions at finite temperatures, in certain ranges of the concentrationp. It is further argued that this behaviour is a quite common feature for spin glass systems characterized by competing interactions.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

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.     

Parking Cars with Spin but no Length

The car parking problem is a one-dimensional model of random packing. Cars arrive to park on a block of length x, sequentially. Each car has, independently, spin up or spin down, w.p. 0 < p 1, for spin up and q = 1 – p for spin down, respectively. Each car tries to park at a uniformly distributed random point t [0, x]. If t is within distance 1 of the location of a previously parked car of the same spin, or within distance a of the location of a previously parked car of the opposite spin, then the new car leaves without parking and the next car arrives, until saturation. We study the problem analytically as well as numerically. The expected number of up spins c(p, a) per unit length for sufficiently large x is neither monotonic in p for fixed a, nor is it monotone in a for fixed p, in general. An intuitive explanation is given for this nonmonotonicity.     

Reentrant transitions in the van Hemmen model of a spin glass

The van Hemmen model of a spin glass, which is an Ising model with random couplings J_ij between sites i and j equal to J₀ + J(ξ_iη_j + ξ_jη_i), where (ξ_i, η_i) are independent, identically distributed random variables, is studied in the pair approximation of the cluster variation method. For the family of probability distributions (1 − p)δ(ξ_i − a) + pδ(ξ_i) + (1 − p)δ(ξ_i + a), where p is varied, phase diagrams are constructed. They are qualitatively different from the mean-field phase diagrams and display a competition between tendencies towards spin-glass and towards ferromagnetic ordering, which results in reentrant transitions. It is argued that the observed effects are not accidental but are borne by the competition of bonds of the underlying lattice system.     

Bond percolation with parallelism restriction on square lattices

As a simple approximation for the ±J spin glass we studied bond percolation on square lattices. However, two neighboring chains of ferromagnetic bonds are required for spins to be regarded as connected. We determine the percolation thresholdp _c =0.8282±0.0002 and the critical exponent =0.75 _–0.05 ^+0.02 for this specific percolation by means of Monte-Carlo simulation on square lattices (up to 150×150).     

Frustrated percolation,spin glasses and glasses

Summary The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT _p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT _g in the same universality class of the Ising spin glass model. AboveT _p the time-dependent autocorrelation function is characterized by a single exponential, while forT _p>T>T _g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT _g the system is in glassy state with an infinitely long relaxation time. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Exact ground states of two-dimensional ±J Ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE _0.5 =–1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.     

Phase diagram of a simple model of Eu p Sr1−p S

A random site Ising model on the checkerboard square lattice with first neighbor interactionsJ in all first neighbor bonds and second neighbor interactionsJ in red squares is considered as a simple model of the dilute spin glass of Eu _p Sr_1–p S. The phase boundary between the paramagnetic and ferromagnetic phases, and that between the paramagnetic and spin glass phases are calculated. The obtained phase diagram is qualitatively similar to the experimental result by Maletta and Convert.     

Nuclear and hadronic reaction mechanisms producing spin asymmetry

We briefly review concept of the quark recombination (QRC) model and a general success of the model. To solve the existing problem, so called anomalous spin observables, in the high energy hyperon spin phenomena, we propose a mechanism; the primarily produced quarks, which are predominantly u and d quarks, act as the leading partons to form the hyperons. Extension of the quark recombination concept with this mechanism is successful in providing a good account of the anomalous spin observables. Another kind of anomaly, the non-zero analysing power and spin depolarization in the Λ hyperon productions, are also discussed and well understood by the presently proposed mechanism. Recently, a further difficulty was observed in an exclusive ΛK ⁺ p production and wel will indicate a possible diagram for resolving it.     

Universality of the REM for Dynamics of Mean-Field Spin Glasses

We consider a version of Glauber dynamics for a p-spin Sherrington– Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the N-dimensional hypercube. We show that, for all p ≥ 3 and all inverse temperatures β > 0, there exists a constant γ _{β ,p}  > 0, such that for all exponential time scales, exp(γ N), with γ < γ _{β ,p} , the properly rescaled clock process (time-change process) converges to an α-stable subordinator where α = γ/β ² < 1. Moreover, the dynamics exhibits aging at these time scales with a time-time correlation function converging to the arcsine law of this α-stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system) the dynamics of p-spin models ages in the same way as the REM, and by extension Bouchaud’s REM-like trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case p = 2) seems to belong to a different universality class.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Critical behavior of short range Potts glasses

We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form exp(const.T ^–2), and an algebraic singularity atT0.25 ind=4. We conclude that the lower critical dimension of the present model isd _c =3 or very close to it. Some of the critical exponents are estimated and their respective values discussed.     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Spin-dependent photoabsorption at theL-edges of ferromagnetic Gd and Tb metal

The spin-dependent absorption of circularly polarized x-rays is studied at theL-edges of ferromagnetic Gd and Tb metal. At theL ₁-edge a spin-dependent part of the absorption coefficient of 10^–3–10^–2 is observed. Strong resonance absorption known as white line occurs at theL ₂- andL ₃-absorption onset. Correlated with it one finds large spin-dependent absorption effects with amplitudes of a few percent. The spin-dependent absorption spectra reflect the profiles of the spin densities of the states populated in the absorption process. Thep-states show spin densities correlated with the first two flat bands above the Fermi level. The spin density of thed-like states is concentrated in the energy range of the white line. In Gd a splitting of (0.5–0.6) eV of the unoccupied 5d spin up and spin down bands is indicated for both spin-orbit partners. In Tb a large dependence of the 5d spin density on the spin-orbit configuration is observed. The experimental results on the spin densities in Gd are compared with band structure calculations for the ferromagnetic ground-state. The theoretical and experimental spin density profiles agree well for thep-states but not for thed-states. The discrepancy concerning thed-states may be attributed to core-hole polarization effects in the absorption process.     

Transverse magnetic ordering

There is an increasing number of ferromagnets and antiferromagnets which are observed to undergo either a further long range magnetic order or spin glass transition in components of the moment transverse to either the ferromagnetic or antiferromagnetic ordering direction. Necessary conditions include exchange frustration and some atomic disorder. We discuss the observation of transverse antiferromagnetic order in the ferromagnet (Fe, Mn)₃Si and the transverse spin glass phase observed in the ferromagnetic glassy metal a-(Fe, Zr) and the antiferromagnet γ-Mn–Cu.     

Influence of quenched nonmagnetic impurities on phase transitions in a three-dimensional diluted Potts model with spin state number q = 4

The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure (p = 1.00) and weakly diluted (p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.     

Demonstration of electrical spin injection into a semiconductor using a semimagnetic spin aligner

Spin injection into semiconductors has been a field of growing interest during recent years, because of the large possibilities in basic physics and for device applications that a controlled manipulation of the electrons spin would enable. However, it has proven very difficult to realize such a spin injector experimentally. Here we demonstrate electrical spin injection and detection in a GaAs/AlGaAs p-i-n diode using a semimagnetic II–VI semiconductor (Zn_{1 − x − y}Be_xMn_ySe) as a spin aligner. The degree of circular polarization of the electroluminescence from the diode is related to the spin polarization of the conduction electrons. Thus, it may be used as a detector for injected spin-polarized carriers. Our experimental results indicate a spin polarization of the injected electrons of up to 90% and are reproduced for several samples. The degree of optical polarization depends strongly on the Mn concentration and the thickness of the spin aligner. Electroluminescence from a reference sample without spin aligner as well as photoluminescence after unpolarized excitation in the spin aligner sample show only the intrinsic polarization in an external magnetic field due to the GaAs bandstructure. We can thus exclude side effects from Faraday effect or magnetic circular dichroism in the semimagnetic layer as the origin of the observed circularly polarized electroluminescence.