Showing papers in "Lecture Notes in Physics in 1987"

Scaling theory of the ordered phase of spin glasses

Abstract: The ordered phase of short-range spin glasses is described in terms of the scaling behaviour associated with a zero-temperature fixed point. The main ingredient of the theory is the exponent y which describes the growth with length scale L of the characteristic coupling at zero temperature, J(L) − JLY. The exponent y is estimated numerically for dimensions d=2,3. For Ising spin glasses we find y − -0.3 for d=2 and y − 0.2 for d=3, implying scaling to weak (strong) coupling for d=2(3), i.e. the “lower critical dimension” dl satisfies 2 dl it determines the large scale properties of the ordered phase, such as the long-distance behaviour of connected correlation functions, G(r) ∝ r−y, and the singular response to a weak magnetic field, msing ∝ hd/(d-2y), The decay of the connected correlation functions at large distances implies that the pure-state overlap distribution function P(q) is trivial, in contrast to the Sherrington-Kirkpatrick model. The dynamics of the system are also discussed, as is the extension to vector spin models.

The Theory of Neural Networks: The Hebb Rule and Beyond

Abstract: Recent studies of the statistical mechanics of neural network models of associative memory are reviewed The paper discusses models which have an energy function but depart from the simple Hebb rule This includes networks with static synaptic noise, dilute networks and synapses that are nonlinear functions of the Hebb rule (eg, clipped networks) The properties of networks that employ the projection method are reviewed

Irreversible spin glasses and neural networks

Abstract: We study the way in which the properties of spin glasses and associative memory networks are changed when the interactions between the units are not symmetrical. Our models are analog networks subject to thermal noise (Langevin models). In an approximation which becomes exact in the limit of large spin dimensionality, we find that spin glass phases are suppressed, even for arbitrarily small asymmetry. However, in the associative networks, memory states are not seriously degraded; their critical temperature is simply lowered from its value in the corresponding symmetric model. The effect of making the number of memories a finite fraction of the number of units in the system is also qualitatively the same as in the symmetric case. We suggest that asymmetric couplings may make retrieval of the desired memory states faster, since the system will not get trapped in spin glass states.

Calculating exact ground states of spin glasses: A polyhedral approach

Abstract: In this paper we describe recent developments in the theory and algorithm design of combinatorial optimization that are related to questions concerning ground states of spin glasses. In particular, we outline an approach, based on polyhedral combinatorics, that has led to the implementation of a cutting plane method for calculating exact ground states of spin glasses in the Ising model. With this method exact ground states for planar grids of size up to 40 x 40 with periodic boundary conditions and exterior magnetic field can be determined in reasonable running times.

Solar an stellar coronae

Abstract: This paper reviews our present understanding of coronal heating, structuring and variability that has emerged from space observations of the Sun and nearby stars. It is shown that a basic analogy exists between solar coronal physics and the phenomena observed in the coronae of other late-type stars. Recent X-ray observations of stellar coronae from EXOSAT are used to illustrate the main points.

Solar and stellar convection

Abstract: We examine the progress made during the last decade in our knowledge of stellar convection, first in the theory and using numerical simulation, and second through observations, from ground and space.

Spin-glasses, optimization and neural networks

Abstract: In the spirit of the Colloquium, the connections between Spin-glasses, Optimization problems and Neural Networks are outlined. Special emphasis is given on recent work on phase transition in spin-glasses. A complete cooling recipe for “spin-glass-like” optimization problems is given. The application of numerical spin-glass and optimization techniques to neural network problems is shown.

Diffusion in ultrametric spaces

Abstract: In this review we discuss the diffusion in ultrametric spaces and analyze the long time behaviour of characteristic observables, e.g. the autocorrelation function. We consider both models with stochastic and nonstochastic parameters (branching ratios, transition rates). Furthermore, results for random energy and random free energy models are given.

Stellar vs. solar activity: The case of pre-main sequence stars

Abstract: X-rays have proved a powerful tool in discovering, or monitoring, the activity of many kinds of stars Among these, the T Tauri stars and other pre-main sequence objects are particularly interesting in that, based on X-rays, the activity seems to be of solar type, albeit on a scale 103 to 106 times higher in intensity, mainly in the form of gigantic flares Also, in the radio range, follow-up observations have allowed to discover a few flaring PMS stars Optical results (multi-band photometry) have recently confirmed the solar nature of this activity to some extent, by revealing periodic variations attributed to large starspots In addition, from these data and other rotation indicators, one finds a fair correlation between rotation and activity, as can be expected from dynamo-induced phenomena already known on the Sun

Solar and stellar chromospheres

Abstract: This review attempts to highlight two fundamental and complementary aspects of the chromospheric phenomenon; viz., global properties of stellar chromospheres and their variation among the stars, and the underlying fine structure that affects or determines these global properties. After an introductory discussion of the gross vertical structure of a stellar chromosphere, attention is given to the chromospheric geometric extent and its dependence on the position of the star in the HR diagram. This includes a critical review of various explanations of the dividing line that separates red giants from Solar-like stars. A subsequent chapter summarizes main features of proposed chromospheric heating mechanisms and discusses the role that magnetic fields play in the transport and dissipation of energy. The onset of stellar chromospheres and the magnitude of nonthermal motions can be probed by the Wilson-Bappu effect and by similar empirical results. The well-known insensitivity of the CaIIK line width to the stellar activity level might be largely due to a collective effect. The final chapter explores the dependence of chromospheric magnetic fine structure on global stellar properties.

Stellar activity and rotation

Abstract: The most important signatures and parameters of stellar magnetic activity and their relation with global stellar parameters are briefly reviewed with the aim of indicating which are the most significant data that are required to constrain possible models of stellar activity. The sporadic and cyclic variability aspect is, particularly stressed, firstly, because it is a crucial activity parameter and, secondly, because of its possible effects. on the derived general correlations between activity and stellar parameters. In particular, the rotation rate, although it is recognized to play a relevant role, still its correlation with various activity indicators has an essentially qualitative character, because other global stellar parameters undergo concurrent changes, making it difficult to isolate the pure effect of stellar rotation from observations.

Nickel clusters as surface models for adsorption

Abstract: Self-consistent charge Xα calculations of the electronic properties of nickel clusters up to 19 atoms are reported The geometries were chosen according to adsorption sites and represent (100), (110) nickel surfaces, and bulk nickel

Numerical studies of spin glasses

Abstract: We survey the progress in numerical studies of spin glasses since the first Heidelberg Colloquium, and discuss the resulting advances in our understanding of the field. A clear case can be made for the importance of using multiple methods of attack for the same problem. Combination methods, e.g. finite size scaling and Monte Carlo simulations, which we cover in some detail, are found to be particularly useful. Some remaining outstanding issues are raised, and directions for future work suggested.

Dynamics of the formation of ordered domains out of initially disordered configurations

Abstract: This talk reviews phenomenological theories and Monte Carlo simulations on the dynamics of ordering processes, and the associated statistical fluctuations, both in pure systems and in systems with quenched disorder. Particular attention is paid to understand size effects and the approach to the thermodynamic limit: we discuss time-scales on which fluctuations around an equilibrium state decay, the time-scale for growth of a domain size comparable to the system volume, and the “ergodic time” on which a system dynamically averages over its various ordered configurations.

New ideas about granulation based on data from the solar optical universal polarimeter instrument on spacelab 2 and magnetic data from big bear solar observatory

Abstract: The Solar Optical Universal Polarimeter (SOUP) on Spacelab 2 collected time sequences of diffraction limited (0.5 are second) granulation images with excellent pointing (.003 arc seconds) and freedom from the distortion that plagues groundbased images. The solar 5 minute oscillations are clearly seen in the data. Using Fourier transforms in the temporal and spatial domains, we have shown that oscillations have an important effect on the autocorrelation (AC) lifetime. When the oscillations are removed the autocorrelation lifetime is found to increase from 270 seconds to 410 and 890 seconds in quiet and magnetic regions, respectively. Exploding granules are common and it is hard to find a granule that neither explodes nor is unaffected by an nearby explosion. We speculate that a significant fraction of granule lifetimes are terminated by nearby explosions. Via local correlation tracking techniques we have been able to measure horizontal displacements, and thus transverse velocities, in the intensity field. It is possible to detect both super and mesogranulation. Horizontal velocities are as great as 1000 m/s in quiet sun and the average velocity is 400 m/s and 100 m/s in quiet and magnetic sun, respectively. These flow fields affect the measured AC lifetimes. After correcting for steady flow, we estimate a lower limit to the lifetime in quiet and magnetic sun to be 440 and 950 seconds, respectively. The SOUP flow fields have been compared with carefully aligned magnetograms taken at the Big Bear Solar Observatory (BBSO) before, during, and after the SOUP images. The magnetic field is observed to exist in locations where either the flow is convergent or on the boundaries of the outflow from a flow cell center. Streamlines calculated from the flow field agree very well with the observed motions of the magnetic field in the BBSO magnetogram movies.

Observations from space vs. ground based observations: Advantages and disadvantages

Abstract: A comparison of observations from space and from the ground should be limited to the optical spectral range (about 0.35μ-10μ). Optical observations give, either directly or indirectly, access to:

Short-term memory

Abstract: This is a rather bold attempt to bridge the gap between neuron structure and psychological data. We try to answer the question: Is there a relation between the neuronal connectivity in the human cortex (around 5,000) and the short-term memory capacity (7±2)? Our starting point is the Hopfield model (Hopfield 1982), presented in this volume by D.J. Amit.

Computer simulation of pretransitional phenomena in Hard-core models for liquid crystals

Abstract: In this paper I have tried to demonstrate that model systems consisting of non-spherical hard-core particles have a surprisingly rich phase diagram. In the case of hard ellipsoids, we found that the stability of the nematic phase is simply related to the degree of non-sphericity of the molecules. Moreover, even though parallel ellipsoidal particles cannot form stable smectics, parallel spherocylinders can. This result is quite unexpected because of the apparent similarity of long spherocylinders and needlelike ellipsoids.

What can the sun tell us about stellar activity

Abstract: The solar-stellar connection relates high-resolution synoptic solar observations to observations of magnetic activity in stars with different rotation rates and internal structures. Our knowledge of magnetic fields in stellar convection zones is based on detailed observations of field structures in the Sun but recent measurements of magnetic activity in other late-type stars have extended our understanding of the solar dynamo. These observations have stimulated detailed modelling of processes associated with magnetic activity. Modulation of activity cycles in slowly rotating stars can be inferred from terrestrial data extending over the last 104 years, while the evolution of the Sun's magnetic field can be inferred from the behaviour of younger stars.

Magnons in spin-glasses in zero-field and in high magnetic fields: Experiments and theory

Abstract: Recent measurements of the specific heat and of the thermal conductivity of Eux Sr1−xS in high magnetic fields are reviewed. In the spin-glass and ferromagnetic concentration ranges the specific heat can be quantitavively accounted for in terms of magnon-like excitations, as shown by numerical calculations without any fit parameter. In particular, the exponential decrease of the magnetic specific heat with decreasing temperature in high fields, indicating a gap in the magnetic excitation spectrum, is reproduced. In the spin-glass range, heat transport is strongly facilitated by an external magnetic field, while below the percolation threshold xp = 0.13 no field effect on the thermal conductivity is seen.