Measuring overlaps in mesoscopic spin glasses via conductance fluctuations

We consider the electronic transport in a mesoscopic metallic spin glass. We show that the distribution of overlaps between spin configurations can be inferred from the reduction of the conductance fluctuations by the magnetic impurities. Using this property, we propose new experimental protocols to probe spin glasses directly through their overlaps.     

Extreme value statistics distributions in spin glasses

We study the probability distribution of the pseudocritical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudocritical point and the extreme value statistics of random variables. For the Sherrington-Kirkpatrick model, both with Gaussian and binary couplings, the distribution of the pseudocritical temperature is found to be the Tracy-Widom distribution. For the EA model, the distribution is found to be the Gumbel distribution. Being the EA model representative of uniaxial magnetic materials with quenched disorder like Fe(0.5)Mn)0.5)TiO(3) or Eu(0.5)Ba(0.5)MnO(3), its pseudocritical point distribution should be a priori experimentally accessible.     

On mean field equations for spin glasses

In this paper we study rigorously the random Ising model on a Cayley tree in the limit of infinite coordination numberz 8. An iterative scheme is developed relating mean magnetizations and mean square magnetizations of successive shells far removed from the surface of the lattice. In this way we obtain local properties of the model in the (thermodynamic) limit of an infinite number of shells. When the coupling constants are independent Gaussian random variables the SK expressions emerge as stable fixed points of our scheme and provide a valid local mean-field theory of spin glasses in which negative local entropy (at low temperatures) while perfectly possible mathematically may still perhaps be physically undesirable. Finally we examine the TAP equations and show that if the average over bond disorder and the limitz 8 are actually performed, one recovers our iterative scheme and hence the SK equations also in the thermodynamic limit.On leave from Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia.     

Zero field muon spin relaxation in simple magnets and spin glasses

A theory is developed for the calculation of zero field muon spin relaxation function for classical simple magnets (Ising, XY, and Heisenberg) in D(=1,2,3) dimensions. The results are different from the Kubo-Toyabe theory, except for Heisenberg system in three dimension. Relation between the relaxation function and random field distribution is dicussed and a new method of analysing experimental data is suggested and discussed in the context of spin glasses.     

Mean field spin glasses treated with PDE techniques

Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1–RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition). Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra’s broken replica measures), whose interest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi.     

On the dynamic mean field theory of spin glasses

We derive in detail Sompolinsky's mean field theory of spin glasses using a diagram expansion of the effective local Langevin equation of Sompolinsky and Zippelius. We use a simpler generating functional than in the literature, on which the quenched average is very easily done. We pay special attention to the existence of an external field. We show that there are two different types of singularities for ω=0 in the equations. The first type, which leads to Parisi'sq(0), is connected with the local magnetisation. The second type, which leads toq′(x), is connected with the nonergodic behaviour. We show that the continuous limit of discrete Sompolinsky solutions has to be taken in order to be in accordance with the fluctuation dissipation theorem on infinite time scales. We discuss carefully the question of dynamical stability. We show that Sommers' solution is unstable only on an infinite time scale and thus remains an acceptable equilibrium theory with a broken symmetry. We argue that for ω=0 a formal violation of the fluctuation dissipation theorem is physically expected if the relaxation times are of the order of the switching time of the external field. From this point of view the spin-glass state is a steady state but not a real equilibrium state.     

Behavior of Ising spin glasses in a magnetic field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.     

Nonequilibrium properties of re-entrant spin glasses in a magnetic field

In this paper the authors discuss how the re-entrant spin-glass state arises in the disordered alloys Ni_100−x Mn_x (x=19, 21, 23), along with the nonequilibrium magnetic properties of these alloys. It is shown that near the Gabay-Toulouse phase line the time it takes the system to reach equilibrium is comparable to times required to perform static experiments (10¹–10⁴ s); cooling the sample into the region of crossover with the de Almeida-Thouless line causes these times to increase to astronomical values of more than 10¹⁶ s. A method is proposed for constructing magnetic phase diagrams of systems of this type in “magnetic field-temperature” coordinates. Fiz. Tverd. Tela (St. Petersburg) 41, 2028–2033 (November 1999)     

On the connection between spin glasses and gauge field theories

A simple connection between Ising spin glasses and the Z₂ lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature properties (e.g. a negative entropy), which are related to a temperature dependence of the frustration. A restricted annealing scheme is presented which remedies this deficiency through the introduction of a pure gauge coupling counterterm. The possible phase diagrams of the lattice gauge system and their relevance to spin glass transitions are discussed.     

Spin-to-charge conversion of mesoscopic spin currents

Recent theoretical investigations have shown that spin currents can be generated by passing electric currents through spin-orbit coupled mesoscopic systems. Measuring these spin currents has, however, not been achieved to date. We show how mesoscopic spin currents in lateral heterostructures can be measured with a single-channel voltage probe. In the presence of a spin current, the charge current I(qpc) through the quantum point contact connecting the probe is odd in an externally applied Zeeman field B, while it is even in the absence of spin current. Furthermore, the zero-field derivative ?(B)I(qpc) is proportional to the magnitude of the spin current, with a proportionality coefficient that can be determined in an independent measurement. We confirm these findings numerically.     

Insulating spin glasses

The possibility of obtaining spin glasses by addition of impurities in an antiferromagnetic insulator is examined. Dipolar interactions are briefly considered but the attention is focussed on Heisenberg systems. Equivalence with the Edwards-Anderson model is derived in a theoretical case. Experimental realisations, such as quasi-one dimensional systems, and spinels, are reviewed. A weak concentration of non-magnetic impurities can give rise to a new state that we call semi spin glass, in which a ferromagnetic component coexists with a transverse, spin glass component. An important case is when the pure system has a high ground state degeneracy (cooperative paramagnet). Non-magnetic impurities or other forms of disorder can transform it into a spin glass.     

Thermopower of spin glasses

We calculate the thermopowerS _d(T) of spin glasses on the basis of thesd exchange model with additional interactions between the impurity spins by means of time dependent perturbation theory. Similarly to the Kondo effect, the observed giant thermopower can only be explained if one also takes into account the spin independent interactionV between the magnetic impurities and the conduction electrons. We obtain a Kondo termS _d ⁽¹⁾ (T) (which reduces for vanishing spin interactions to the thermopower of Kondo systems) and in addition a resonance termS _d ⁽²⁾ (T) of opposite sign which vanishes for vanishing interactions. The superposition of both terms leads to an additional extremum of the total thermopower and to a change of sign at a temperatureT ₀ which depends on the Kondo temperature and on the magnetic excitations of the spin glass and therewith on the freezing temperatureT _f. We obtain at low temperatures for oscillating and relaxing spin glass modesS _d ⁽¹⁾ T² andS _d ⁽²⁾ T. At high temperaturesS _d ⁽¹⁾ (T) decreases as |lnT|^–3 andS _d ⁽²⁾ asT ^–1. A close relationship between the temperature dependent resistivity in Born approximation andS _d ⁽¹⁾ (T) is pointed out.SFB 125 Aachen-Jülich-Köln     

Superconductivity of spin glasses

The coexistence of superconducting and spin glass phases is investigated. The dependence of the phase transition temperature in the spin glass state both on the impurity concentration and the superconductivity state is given. The influence of the spin glass phase on the renormalized frequency and the order parameter of the conduction electrons is determined.     

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.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln