The Sherrington-Kirkpatrick spin glass model in the presence of a random field with a joint Gaussian probability density function for the exchange interactions and random fields

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington-Kirkpatrick Ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method. The two random variables (exchange integral interaction and random magnetic field) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient $\rho$. The thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density. The de Almeida-Thouless line is explored as a function of temperature, $\rho$ and other system parameters. The entropy for zero temperature as well as for non zero temperatures is partly negative or positive, acquiring positive branches as $h_{0}$ increases.Comment: 30 pages, 11 figures. arXiv admin note: text overlap with arXiv:cond-mat/0504615 by other author

The random field Ising model with an asymmetric and anisotropic trimodal probability distribution

The Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution $P(h_{i})=p\; \delta(h_{i}-h_{0}) + q \delta (h_{i}+ \lambda *h_{0}) + r \delta (h_{i})$, is investigated. The partial probabilities $p, q, r$ take on values within the interval $[0,1]$ consistent with the constraint $p+q+r=1$, asymmetric distribution, $h_{i}$ is the random field variable with basic absolute value $h_{0}$ (strength); $\lambda$ is the competition parameter, which is the ratio between the respective strength of the random magnetic field in the two principal directions $(+z)$ and $(-z)$ and is positive so that the random fields are competing, anisotropic distribution. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays mainly second order phase transitions, which, for some values of $p, q$ and $h_{0}$, are followed by first order phase transitions joined smoothly by a tricritical point; occasionally, two tricritical points appear implying another second order phase transition. In addition to these points, re-entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of $\lambda$, $p$ and $q$. Using the variational principle, we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to $h_{0}$, considered as an independent variable in addition to the temperature.Comment: 30 pages, 8 figure

Uncovering the secrets of the 2d random-bond Blume-Capel model

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the system onto a network and we search for a minimum cut by a maximum flow method. In finite temperatures the system is studied by an efficient two-stage Wang-Landau (WL) method for several values of the crystal field, including both the first- and second-order phase transition regimes of the pure model. We attempt to explain the enhancement of ferromagnetic order and we discuss the critical behavior of the random-bond model. Our results provide evidence for a strong violation of universality along the second-order phase transition line of the random-bond version.Comment: 6 LATEX pages, 3 EPS figures, Presented by AM at the symposium "Trajectories and Friends" in honor of Nihat Berker, MIT, October 200

Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond d=2d=2 Blume-Capel model

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.Comment: 12 pages, 11 figures, submitted for publicatio

Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness

We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with \nu=1.30(6) and \beta/\nu=0.128(5). This amounts to a strong violation of the universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two transitions supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.Comment: Added discussion and references. 10 pages, 6 figures. Published versio

Wetting of Curved Surfaces

As a first step towards a microscopic understanding of the effective interaction between colloidal particles suspended in a solvent we study the wetting behavior of one-component fluids at spheres and fibers. We describe these phenomena within density functional theory which keeps track of the microscopic interaction potentials governing these systems. In particular we properly take into account the power-law decay of both the fluid-fluid interaction potentials and the substrate potentials. The thicknesses of the wetting films as a function of temperature and chemical potential as well as the wetting phase diagrams are determined by minimizing an effective interface potential which we obtain by applying a sharp-kink approximation to the density functional. We compare our results with previous approaches to this problem.Comment: 54 pages, 17 figures, accepted for publication in Physica

A comparative study of the dynamic critical behavior of the four-state Potts like models

We investigate the short-time critical dynamics of the Baxter-Wu (BW) and $n=3$ Turban (3TU) models to estimate their global persistence exponent $\theta _{g}$. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations. In addition, we estimate again the dynamical exponents of the four-state Potts (FSP) model in order to compare them with results previously obtained for the BW and 3TU models and to decide between two sets of estimates presented in the current literature. We also revisit the short-time dynamics of the 3TU model in order to check if, as already found for the FSP model, the anomalous dimension of the initial magnetization $x_{0}$ could be equal to zero

Wetting of a symmetrical binary fluid mixture on a wall

We study the wetting behaviour of a symmetrical binary fluid below the demixing temperature at a non-selective attractive wall. Although it demixes in the bulk, a sufficiently thin liquid film remains mixed. On approaching liquid/vapour coexistence, however, the thickness of the liquid film increases and it may demix and then wet the substrate. We show that the wetting properties are determined by an interplay of the two length scales related to the density and the composition fluctuations. The problem is analysed within the framework of a generic two component Ginzburg-Landau functional (appropriate for systems with short-ranged interactions). This functional is minimized both numerically and analytically within a piecewise parabolic potential approximation. A number of novel surface transitions are found, including first order demixing and prewetting, continuous demixing, a tricritical point connecting the two regimes, or a critical end point beyond which the prewetting line separates a strongly and a weakly demixed film. Our results are supported by detailed Monte Carlo simulations of a symmetrical binary Lennard-Jones fluid at an attractive wall.Comment: submitted to Phys. Rev.

Quenched bond randomness in marginal and non-marginal Ising spin models in 2D

We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied and their general universality aspects are inspected by a detailed finite-size scaling (FSS) analysis. We find that, the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties for a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. Yet, a careful FSS analysis of our data favors the field-theoretically predicted logarithmic corrections.Comment: 19 pages, 5 figures, final versio