The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte

Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe

Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses

A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are treated. A ``ballistic-search'' algorithm is applied which allows even for large system sizes to identify clusters of ground states which are connected by chains of zero-energy flips of spins. The number of clusters n_C diverges with N going to infinity. For all dimensions considered here, an exponential increase of n_C appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B (3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference

Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth

Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett. {\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate analytically the asymptotic scaled capture-number distribution (CND) for one-dimensional irreversible submonolayer growth of point islands. The predicted asymptotic CND is in reasonably good agreement with kinetic Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic} scaled island-size distribution (ISD). We then show that a slight modification of our analytical form leads to an analytic expression for the asymptotic CND and a resulting asymptotic ISD which are in excellent agreement with KMC simulations. We also show that in the asymptotic limit the self-averaging property of the capture zones holds exactly while the asymptotic scaled gap distribution is equal to the scaled CND.Comment: 4 pages, 1 figure, submitted to Phys. Rev.

Carrier induced ferromagnetism in diluted magnetic semi-conductors

We present a theory for carrier induced ferromagnetism in diluted magnetic semi-conductor (DMS). Our approach treats on equal footing quantum fluctuations within the RPA approximation and disorder within CPA. This method allows for the calculation of $T_c$, magnetization and magnon spectrum as a function of hole, impurity concentration and temperature. It is shown that, sufficiently close to $T_c$, and within our decoupling scheme (Tyablicov type) the CPA for the itinerant electron gas reduces to the Virtual Crystal Approximation. This allows, in the low impurity concentration and low density of carriers to provide analytical expression for $T_c$. For illustration, we consider the case of $Ga_{1-c}Mn_{c}As$ and compare our results with available experimental data.Comment: 5 figures included. to appear in Phys. Rev. B (brief report

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction across a tunneling junction out of equilibrium

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic $s$-$d$ spin impurities across a tunneling junction is studied when the system is driven out of equilibrium through biasing the junction. The nonequilibrium situation is handled with the Keldysh time-loop perturbation formalism in conjunction with appropriate coupling methods for tunneling systems due to Caroli and Feuchtwang. We find that the presence of a nonequilibrium bias across the junction leads to an interference of several fundamental oscillations, such that in this tunneling geometry, it is possible to tune the interaction between ferromagnetic and antiferromagnetic coupling at a fixed impurity configuration, simply by changing the bias across the junction. Furthermore, it is shown that the range of the RKKY interaction is altered out of equilibrium, such that in particular the interaction energy between two slabs of spins scales extensively with the thickness of the slabs in the presence of an applied bias.Comment: 38 pages revtex preprint; 5 postscript figures; submitted to Phys. Rev.

Ohm's Law for Plasma in General Relativity and Cowling's Theorem

The general-relativistic Ohm's law for a two-component plasma which includes the gravitomagnetic force terms even in the case of quasi-neutrality has been derived. The equations that describe the electromagnetic processes in a plasma surrounding a neutron star are obtained by using the general relativistic form of Maxwell equations in a geometry of slow rotating gravitational object. In addition to the general-relativistic effect first discussed by Khanna \& Camenzind (1996) we predict a mechanism of the generation of azimuthal current under the general relativistic effect of dragging of inertial frames on radial current in a plasma around neutron star. The azimuthal current being proportional to the angular velocity $\omega$ of the dragging of inertial frames can give valuable contribution on the evolution of the stellar magnetic field if $\omega$ exceeds $2.7\times 10^{17} (n/\sigma) \textrm{s}^{-1}$ ($n$ is the number density of the charged particles, $\sigma$ is the conductivity of plasma). Thus in general relativity a rotating neutron star, embedded in plasma, can in principle generate axial-symmetric magnetic fields even in axisymmetry. However, classical Cowling's antidynamo theorem, according to which a stationary axial-symmetric magnetic field can not be sustained against ohmic diffusion, has to be hold in the general-relativistic case for the typical plasma being responsible for the rotating neutron star.Comment: Accepted for publication in Astrophysics & Space Scienc

Particle acceleration in three-dimensional tearing configurations

In three-dimensional electromagnetic configurations that result from unstable resistive tearing modes particles can efficiently be accelerated to relativistic energies. To prove this resistive magnetohydrodynamic simulations are used as input configurations for successive test particle simulations. The simulations show the capability of three-dimensional non-linearly evolved tearing modes to accelerate particles perpendicular to the plane of the reconnecting magnetic field components. The simulations differ considerably from analytical approaches by involving a realistic three-dimensional electric field with a non-homogenous component parallel to the current direction. The resulting particle spectra exhibit strong pitch-angle anisotropies. Typically, about 5-8 % of an initially Maxwellian distribution is accelerated to the maximum energy levels given by the macroscopic generalized electric potential structure. Results are shown for both, non-relativistic particle acceleration that is of interest, e.g., in the context of auroral arcs and solar flares, and relativistic particle energization that is relevant, e.g., in the context of active galactic nuclei.Comment: Physics of Plasmas, in prin

Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model

We consider the random-bond +- J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T*= 0.9527(1), p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T=0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T*, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents nu=1.50(4) and eta=0.128(8), and beta = 0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T*. Our results for the critical exponents are consistent with the hyperscaling relation 2 beta/nu - eta = d - 2 = 0.Comment: 32 pages, added refs and a discussion on hyperscalin