The 3-d Random Field Ising Model at zero temperature

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $L$ in three dimensions. For each random field configuration we vary the ferromagnetic coupling strength $J$. We find that in the infinite volume limit the magnetization is discontinuous in $J$. The energy and its first $J$ derivative are continuous. The approch to the thermodynamic limit is slow, behaving like $L^{-p}$ with $p \sim .8$ for the gaussian distribution of the random field. We also study the bimodal distribution $h_{i} = \pm h$, and we find similar results for the magnetization but with a different value of the exponent $p \sim .6$. This raises the question of the validity of universality for the random field problem.Comment: 8 pages, 3 PostScript Figure

Interface mapping in two-dimensional random lattice models

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface properties of the two models are known to be related by a mapping which is valid in the continuum approximation. Here we consider finite random samples with the same form of disorder for both models and calculate the respective equilibrium states exactly by combinatorial optimization algorithms. We study the evolution of the interfaces with the strength of disorder and analyse and compare the interfaces of the two models in finite lattices.Comment: 7 pages, 6 figure

Critical and tricritical singularities of the three-dimensional random-bond Potts model for large qq

We study the effect of varying strength, $\delta$, of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the spins points into the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\delta>\delta_t$ this percolating cluster coexists with a percolating cluster of non-correlated spins. Such a co-existence is only possible in more than two dimensions. We argue and check numerically that $\delta_t$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as $\beta_t/\nu_t=0.10(2)$ and $\nu_t=0.67(4)$. We claim these exponents are $q$ independent, for sufficiently large $q$. In the second-order transition regime the critical exponents $\beta_t/\nu_t=0.60(2)$ and $\nu_t=0.73(1)$ are independent of the strength of disorder.Comment: 12 pages, 11 figure

Rounding of first-order phase transitions and optimal cooperation in scale-free networks

We consider the ferromagnetic large-$q$ state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: a fraction of $m$ (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically on the Barab\'asi-Albert network. The distribution of finite-size transition points is characterized by a shift exponent, $1/\tilde{\nu}'=.26(1)$, and by a different width exponent, $1/\nu'=.18(1)$, whereas the magnetization at the transition point scales with the size of the network, $N$, as: $m\sim N^{-x}$, with $x=.66(1)$.Comment: 8 pages, 6 figure

Theoretical view on the origin and implications of structural distortions in polyoxometalates

Structural features of polyoxometalates (POMs) —versatile inorganic clusters of academic and technological interest— are discussed in the present article. POMs are, in general, very regular structures presenting a high symmetry in most cases. Distortions are, however, important for some electronic and magnetic properties. We herein discuss some particular geometric features that are crucial for the theoretical treatment and comprehension of well-known experimental phenomena. For instance, we have been able to understand and rationalize the geometrical distortions present in molybdenum POMs. Moreover, we can affirm that these geometrical distortions are caused by a pseudo Jahn Teller effect. In what concerns NMR chemical shifts, we present a discussion on the importance of geometry for the correct description of the signals and the key role played by the interatomic distances. Finally, a study on the adsorption of Keggin clusters on silver surfaces shows how the POM structure looses its regular shape to adapt to that new situation

Density of critical clusters in strips of strongly disordered systems

We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study optimal Fortuin-Kasteleyn clusters by combinatorial optimization algorithm. For the random transverse-field Ising chain clusters are defined and calculated through the strong disorder renormalization group method. The numerically calculated density profiles close to the boundaries are shown to follow scaling predictions. For the random bond Potts model we have obtained accurate numerical estimates for the critical exponents and demonstrated that the density profiles are well described by conformal formulae.Comment: 9 pages, 9 figure

Complexity spectrum of some discrete dynamical systems

We first study birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of $3 \times 3$ matrices. We introduce a semi-numerical analysis which enables to compute the Arnold complexities for all the $9!$ possible birational transformations. These complexities correspond to a spectrum of eighteen algebraic values. We then drastically generalize these results, replacing permutations of the entries by homogeneous polynomial transformations of the entries possibly depending on many parameters. Again it is shown that the associated birational, or even rational, transformations yield algebraic values for their complexities.Comment: 1 LaTex fil

Plasticized Starch/ Tunicin Whiskers Nanocomposites : 1. Structural Analysis

International audienceNanocomposite materials were obtained using glycerol plasticized starch as the matrix and a colloidal suspension of cellulose whiskers as the reinforcing phase. The cellulose whiskers, prepared from tunicin, consisted of slender parallelepiped rods with a high aspect ratio. After mixing the raw materials and gelatinization of starch, the resulting suspension was cast and evaporated under vacuum. The composites were conditioned at various moisture contents in order to evaluate the effect of this parameter on the composite structure. Th

Scale Invariance in disordered systems: the example of the Random Field Ising Model

We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this non perturbative phenomenon is not particular to the RFIM in 3-d. It is generic for disordered systems in two dimensions and may also happen in other three dimensional disordered systems