G. Grinstein

Suppression of tunneling by interference in half-integer-spin particles.

Within a wide class of ferromagnetic and antiferromagnetic systems, quantum tunneling of magnetization direction is spin-parity dependent: it vanishes for magnetic particles with half-integer spin, but is allowed for integer spin. A coherent-state path-integral calculation shows that this topological effect results from interference between tunneling paths.

Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics

We show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the KPZ equation. Numerical simulations in 1d confirm this prediction, and yield other exponents of the multiplicative noise problem. The numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values, and show that the exponent governing the divergence in this range varies continuously with control parameter.

Phase structure of systems with multiplicative noise.

The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero range of parameter values over which the susceptibility is infinite in any dimension. A scaling theory of the strong-coupling transition is constructed.

Quantum tunneling and dissipation in nanometer-scale magnets

Abstract We summarize recent low-temperature noise and AC magnetic susceptibility measurements on the nanometer-scale magnetic protein horse-spleen ferritin. The experiments show a narrow resonance peak at about 10 6 Hz, which is discussed in the framework of recently-developed theories of macroscopic quantum coherence and tunneling in antiferromagnets; theory and experiment are argued to agree qualitatively, though quantitative discrepancies remain. We also review the recent analysis of a rather general spin-parity effect for tunneling in magnetic systems: systems with appropriate symmetry may exhibit quantum tunneling for integer spin, but not for half-odd-integer spin, where destructive interference between different tunneling paths suppresses the tunneling. Finally, we study the effect on this spin-parity phenomenon caused by dissipation, i.e. coupling to an environment consisting of a bath of harmonic oscillators. Using the real-time, Feynman-Vernon path integral formalism, we find models where an arbitrarily small amount of ohmic dissipation completely destroys the spin-parity effect (i.e., produces as such tunneling for half-odd-integer spins as for integer spins), and others where the effect appears to disappear gradually with increasing dissipation. Suprisingly, however, there is a sense in which the spin-parity effect is preserved in both types of models: a Calderia-Leggett type of analysis shows that neither experiences any tunnel splitting of its ground state. We present simple arguments for how this intriguing paradox might be resolved.

Stability of Solid State Reaction Fronts

We analyze the stability of a planar solid-solid interface at which a chemical reaction occurs. Examples include oxidation, nitridation, or silicide formation. Using a continuum model, including a general formula for the stress-dependence of the reaction rate, we show that stress effects can render a planar interface dynamically unstable with respect to perturbations of intermediate wavelength.

Turbulence, power laws and Galilean invariance

Abstract We review current attemps at understanding the scaling behavior of fully developed turbulence through studying simple, scalar, translationally invariant, deterministic coupled-map interface models. The universality classes of such model systems are discussed.

Phase Structure of Systems with Infinite Numbers of Absorbing States

Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to describe the critical behavior of such systems, and also introduce and study a non-Markovian discrete model, which is argued to present the same critical features. On the basis of mean-field analysis, Monte Carlo simulations, and theoretical arguments, we conclude that the phenomenology of the non-Markovian models closely parallels that of systems with many absorbing states in one and two dimensions. The “bulk” or “static” critical properties of these systems fall in the directed percolation (DP) universality class. By contrast, the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior: Depending on parameter values they can, both in one and two dimensions, fall either in the dynamical percolation or DP universality class, or else exhibit apparently nonuniversal exponents. In contrast to previous results, however, the nonuniversal exponents in 2D are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes DP values. These results demonstrate the efficacy of the non-Markovian approach for understanding systems with many absorbing states, which are difficult to analyze in their original microscopic formulation.

Infinite numbers of absorbing states: critical behavior

We briefly review recent progress in elucidating the time-independent critical behavior of systems with infinite numbers of static absorbing states, and show that the critical exponent describing the decay with time of the order parameter right at the critical point is the same as that of the directed percolation problem.

Singular Lyapunov spectra and conservation laws

We give analytic arguments and numerical evidence to show that the presence of conservation laws can produce a singularity in the spectrum of Lyapunov exponents for extended dynamical systems of low spatial dimensionality. This phenomenon can be used, e.g., for finding hidden conservation laws. (c) 1995 American Institute of Physics.

Directed surfaces in disordered media.

The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces, which do not belong to the directed percolation universality class. We formulate a scaling theory of directed surfaces, and calculate critical exponents numerically, using a cellular automaton that locates the directed surfaces without making reference to the dynamics of the underlying interface growth models.