Alan J. Bray

Lower critical dimension of Ising spin glasses: a numerical study

A transfer matrix method is used to study the variation with length scale L of the distribution PL(Jeff) of effective couplings in Ising spin glasses at zero temperature. For a gaussian initial distribution the authors find in two dimensions J(L) identical to ( mod Jeff mod ) varies as L-1 nu / for 2<or=L<or=12, with nu =3.4+or-0.1, implying a zero-temperature phase transition with correlation length exponent nu . In three dimensions the effective couplings initially increase with length scale, J(L) varies as L-1 nu / for 2<or=L<or=4, with -1/ nu approximately=0.2, suggesting a phase transition at finite temperature. The results are described surprisingly well by the zero-temperature version of the Migdal-Kadanoff renormalisation group scheme.

Phase diagrams for dilute spin glasses

A generalised, dilute, infinite-ranged Ising spin-glass model is introduced and studied as a function of the concentration p and temperature T. The phase diagram is investigated and paramagnetic (P), ferromagnetic (F), spin glass (SG) and mixed (M) phases, meeting at a multicritical point (p*,T*), are identified. The P/F and P/SG phase boundaries are derived, and the F/M and M/SG boundaries are calculated close to (p*,T*). The condition for having a re-entrant spin-glass transition is derived. In non-zero magnetic field a p-dependent A-T instability line is obtained. The authors apply their results to the insulator EuxSr1-xS, it is predicted to exhibit re-entrant behaviour.

Persistence and first-passage properties in nonequilibrium systems

In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spin models undergoing phase-ordering dynamics, diffusion equation, fluctuating interfaces, etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalizations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

Metastable states in spin glasses

The number of solutions of the equations of Thouless et al. (1977) is obtained as a function of temperature. The density of solutions with a given free energy is calculated for free energies greater than a (temperature-dependent) critical value.

PERSISTENCE EXPONENTS FOR FLUCTUATING INTERFACES

Numerical and analytic results for the exponent

Global Persistence Exponent for Nonequilibrium Critical Dynamics

\ensuremath{\theta}

Nontrivial Exponent for Simple Diffusion

describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic roughness exponent

Replica theory of quantum spin glasses

\ensuremath{\beta}

Statistics of critical points of Gaussian fields on large-dimensional spaces

, with

Aspect-Ratio Scaling and the Stiffness Exponent θ for Ising Spin Glasses

0l\ensuremath{\beta}l1