Theory of a Heisenberg spin glass

For the quantum mechanical long-range random Heisenberg model we derive mean field equations in analogy to the TAP equations. The complete solution requires a self-consistent calculation of the dynamical local susceptibility. We discuss a variational approximation above and below the critical point.     

Theory of an induced-moment spin glass

We review the derivation of generalised TAP equations for general quantum spin systems and apply the theory to a simple induced-moment spin glass model. We consider two-level systems with a singlet ground state and a triplet excited state, which interact via long range random exchange couplings. For not too large energy splitting the spin glass state can be stabilised.     

Thermodynamic functions of a spin glass

We have measured the specific heats of several dilute ZnMn alloys, and from these results have found simple analytic expressions for the free energy, internal energy, entropy and specific heat of this typical spin glass alloy.     

On a classical spin glass model

A simple, exactly soluble, model of a spin-glass with weakly correlated disorder is presented. It includes both randomness and frustration, but its solution can be obtained without replicas. As the temperatureT is lowered, the spin-glass phase is reached via an equilibrium phase transition atT=T _f . The spin-glass magnetization exhibits a distinctS-shape character, which is indicative of a field-induced transition to a state of higher magnetization above a certain threshold field. For suitable probability distributions of the exchange interactions.

1. A mixed phase is found where spin-glass and ferromagnetism coexist.
2. The zero-field susceptibility has a flat plateau for 0≦T≦T _f and a Curie-Weiss behaviour forT>T _f .
3. At low temperatures the magnetic specific heat is linearly dependent on the temperature.

The physical origin of the dependence upon the probability distributions is explained, and a careful analysis of the ground state structure is given.     

Free energy of a spin glass

We give the theory of a model spin glass of the Sherrington-Kirkpatrick type. Determining that the free energy is given by the potential function of a two-dimensional electrostatic medium, we find exact expressions for this quantity in terms of a multipole expansion of the charge distribution. We also obtain the internal energy, entropy, and specific heat in the form of explicit integrals over the multipole distributions. Pending the outcome of a quantitative investigation into the structure of these functions, here we discuss their properties in a qualitative way.     

A mixed phase transition for a hierarchical spin glass

A proof of the existence of a mixed ferromagnetic (or antiferromagnetic)-spin-glass fixed point for an Ising spin-glass model on the diamond hierarchical lattice is given.     

Quantum parallelism as a tool for ensemble spin dynamics calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.     

Supersymmetric spin glass

The manifestly supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta function form the moduli space ℳ=RP ², where two types of phases are found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase, which may be interpreted as a spin glass phase. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 657–662 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Twist free energy in a spin glass

The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by the breaking of reparametrization invariance of a Parisi type solution. Twisted boundary conditions are thus imposed at two opposite ends of the system in order to study the size dependence of the twist free energy. A loop-expansion is performed to first order around a twisted background. It is found, as expected but it is non trivial, that the theory does renormalize around such backgrounds, as well as for the bulk. However two main differences appear, in comparison with simple ferromagnetic transitions: (i) the loop expansion yields a (negative) anomaly in the size dependence of the free energy, thereby lifting the lower critical dimension to a value greater than two (ii) the free energy is lowered by twisting the boundary conditions. This situation is common in spin glasses, reflecting the non-positivity of mode multiplicity in replica symmetry breaking, but its physical meaning is still unclear. Received 12 April 2002 / Received in final form 30 July 2002 Published online 19 November 2002     

Off-equilibrium fluctuation-dissipation relation in a spin glass

We report new experimental results obtained on the insulating spin glass CdCr_2-2x In_2x S₄. Our experimental setup allows a quantitative comparison between the thermo-remanent magnetisation and the autocorrelation of spontaneous fluctuations of magnetisation, yielding a complete determination of the fluctuation-dissipation relation. The dynamics can be studied both in the quasi-equilibrium regime, where the fluctuation-dissipation theorem holds, and in the deeply ageing regime. The limit of separation of time-scales, as used in analytical calculations, can be approached by use of a scaling procedure.Received: 2 March 2004, Published online: 9 September 2004PACS: 05.70.Ln Nonequilibrium and irreversible thermodynamics - 75.50.Lk Spin glasses and other random magnets - 07.20.Dt Thermometers - 07.55.Jg Magnetometers for susceptibility, magnetic moment, and magnetization measurementsD. Hérisson: Present address: Department of Engineering Sciences - Division of Solid State Physics, Uppsala University, 751 21 Uppsala, SwedenM. Ocio: deceased 21 December 2003     

Exactly solvable model of a spin glass

Sherrington and Kirkpatrick presented a solvable model of a spin glass. In the solution, they used a mathematically unwarranted procedure. In the present article, we show that the problem is exactly solved by starting with the virial expansion formula, and confirm the results of Sherrington and Kirkpatrick. The solution is obtained for the random Ising magnet in which the external field of each site and the exchange integral between each pair of sites are random variables. We obtain the exact thermodynamic properties for this system in the limit of n_w→∞, assuming that the exchange integrals of a spin with O(n_w) neighbours are $\text{O(n}{}_{\mathrm{w}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ and the average value of each is O(n_w^?1). The system is found to show the spin-glass state as well as the paramagnetic and the ferromagnetic state.     

Spin diffusion in a Heisenberg spin glass

Using a combination of analytic and Monte Carlo techniques we obtain estimates for the spin diffusion constant and spin conductivity in a classical simple cubic Heisenberg spin glass which has a Gaussian distribution of exchange interactions between nearest neighbors.     

The order parameter in a spin glass

Various possible precise definitions of an Edwards-Anderson type of order parameter for an Ising model spin glass are considered, using boundary conditions for a finite system, states of an infinite system, and a duplicate-system approach. Several of these definitions are shown to yield identical results.     

Finite block spin phenomenology of spin glass

We herein explain the phase of spin glass by reference to finite block spin theory, in which the phase of the spin glass may be considered as being a ferromagnetic ordering between block spins comprised of random spins that have a majority of individual spins in a given sense. By making use of the Curie law of block spins, we obtained the magnetization, susceptibility, and specific heat for the lower and higher temperature approximations of the Brillouin function. Both the susceptibility and the specific heat thus obtained are in good agreement with existing experimental data, although in the latter case the agreement is less convincing near absolute zero temperature.     

Ground state degeneracy and ferromagnetism in a spin glass

We prove three results for the two-dimensional Ising spin glass model on a square lattice: (a) finite entropy for the ground state; (b) ferromagnetism for low concentrations of antiferromagnetic bonds and low temperatures; (c) vanishing magnetization for a spin glass with equal concentrations of ferro- and antiferromagnetic bonds.     

The simplest spin glass

We study a system of Ising spins with quenched random infinite ranged p-spin interactions. For p → ∞, we can solve this model exactly either by a direct microcanonical argument, or through the introduction of replicas and Parisi's ultrametric ansatz for replica symmetry breaking, or by means of TAP mean field equations. Although the model is extremely simple it retains the characteristic features of a spin glass. We use it to confirm the methods that have been applied in more complicated situations and to explicitlu exhibit the structure of the spin glass phase.     

Vanishing spontaneous magnetization for quantum mechanical models of a spin glass

We prove that the spontaneous magnetization vanishes identically (independently of boundary conditions) for certain quantum mechanical models of a spin glass.