[en] Confronted with the contradiction between mounting evidence for a phase transition in three dimensions with only two states (in zero field) and the necessity for a symmetry breaking a la PARISI when treating an Ising spin glass with a gaussian bond distribution, we look, as an escape, for possible stable replica symmetric solutions, in the tree approximation, associated with non-gaussian distributions

[en] In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

[en] Searching for possible replica symmetric solutions in an Ising spin glass (in the tree approximation) we investigate a toy model whose bond distribution has two non vanishing cumulants (instead of one only as in a gaussian distribution)

[en] The author discusses a recently developed algorithm for simulating statistical systems. The procedure interpolates between molecular dynamics methods and canonical Monte Carlo. The primary advantages are extremely fast simulations of discrete systems such as the Ising model and a relative insensitivity to random number quality. A variation of the algorithm gives rise to a deterministic dynamics for Ising spins. This model may be useful for high speed simulation of non-equilibrium phenomena

[en] We present an exact solution of a one dimensional XY model in a random magnetic field in the limit of strong field pinning. The structure factor exhibits Lorentzian squared behaviour at non-zero temperatures. The scaling behaviour of the correlation length as a function of randomness is different from that obtained in the weak field pinning regime. We also study the dynamical behaviour of the system using a simple relaxational model. The magnetization decays anomalously with time as tsup(7/6) esup(-ctsup(1/3)). (author)

[en] We use the d = 2 Ising model as a concrete example to show that truncation of the derivative matrix T to a subspace S of short-range interactions needs some justification, since each row of T contains arbitrarily large elements in the long-range sector. We point out that despite this a small parameter justifying truncation may exist, we show how to find it, and we perturbatively correct the errors due to truncation, all without leaving S. The bulk of our analysis carries over to other Monte Carlo renormalization-group studies, particularly the d = 3 Ising model

[en] The fact that correlation does not imply causation is well known. Correlation between variables at two sites does not imply that the two sites directly interact, because, e.g., correlation between distant sites may be induced by chaining of correlation between a set of intervening, directly interacting sites. Such 'noncausal correlation' is well understood in statistical physics: an example is long-range order in spin systems, where spins which have only short-range direct interactions, e.g., the Ising model, display correlation at a distance. It is less well recognized that such long-range 'noncausal' correlations can in fact be stronger than the magnitude of any causal correlation induced by direct interactions. We call this phenomenon superadditive correlation (SAC). We demonstrate this counterintuitive phenomenon by explicit examples in (i) a model spin system and (ii) a model continuous variable system, where both models are such that two variables have multiple intervening pathways of indirect interaction. We apply the technique known as decimation to explain SAC as an additive, constructive interference phenomenon between the multiple pathways of indirect interaction. We also explain the effect using a definition of the collective mode describing the intervening spin variables. Finally, we show that the SAC effect is mirrored in information theory, and is true for mutual information measures in addition to correlation measures. Generic complex systems typically exhibit multiple pathways of indirect interaction, making SAC a potentially widespread phenomenon. This affects, e.g., attempts to deduce interactions by examination of correlations, as well as, e.g., hierarchical approximation methods for multivariate probability distributions, which introduce parameters based on successive orders of correlation. copyright 1999 The American Physical Society

[en] A frustration potential is a sum of interactions the terms of which are not simultaneously minimized even in the ground state spin configurations. Such a potential is supposed to occur in spin glasses. The number of ground states which are different only in a finite volume, V, may be 0(exp(|V|)); this is called the existence of a zero point entropy. Ising models with frustration potentials are discussed by the use of contours. The Peierls condition for the phase transition can be properly generalized, taking into account the presence of zero energy contours. The two dimensional case has some special features which we study in detail. (author)

[en] We have studied a Hubbard ring with alternating site potentials for half-filling in presence of a magnetic flux. Using a mean-field approach we have calculated the conductivity of such a ring at low and high temperatures. The interplay of the correlation, the polarizing field and the chemical modulation in site potentials tune the conductivity in an interesting fashion. In presence of the modulation in the site energy an appreciable variation in the conductance is observed with the change in flux. This scenario gets substantially modified in presence of the Hubbard correlation. Finite-size effects are also identified and they are found to be quickly disappearing with increasing system size. Sharp changes in the magnetoconductance is found to disappear at higher temperatures

[en] We study the dynamics of a class of two-dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise. Special lines in the plane of parameters correspond to the Ising model, voter model and majority vote model. The dynamics of this class of models may be described formally in terms of reaction-diffusion processes for a set of coalescing, annihilating, and branching random walkers. We use the freedom allowed by the space of parameters to measure, by numerical simulations, the persistence probability of a generic model in the low-temperature phase, where the system coarsens. This probability is found to decay at large times as a power law with a seemingly constant exponent θ ∼ 0.22. We also discuss the connection between persistence and the nature of the interfaces between domains. (author)