I. A. Hadjiagapiou

Wetting on an attractive compact spherical substrate

The wetting phenomena on a compact spherical substrate of radius R, immersed in an one‐component bulk vapor, are studied as functions of R and e W (a parameter characterizing the adsorbent) within the context of Sullivan’s model. The substrate acts as an external potential V ext(r) on fluid molecules; V ext(r) is found by integrating over the adsorbent’s volume and its strength depends strongly on R. The fluid molecules are of constant diameter d. The density functional theory is used to analyze the structure of the wall–vapor interface by properly generalizing Sullivan’s model. For any value of R, the substrate is either incompletely wet or nonwet; the density profiles, labeled by e W , display only one growth mode, that from thin to thick film as e W increases (in this case adsorption is always positive); for larger values of R, but small e W ’s, there is, in addition, another transition from nonwetting to wetting,adsorption now changes from negative to positive as e W increases. In all cases, the thickness l of the wetting layer grown on the substrate is of the order of ln R. In conclusion, the effect of a spherical substrate on an one‐component bulk vapor in comparison with that of a planar substrate is to reduce the three wetting classes of the planar adsorbent to two which are identified with class III, nonwetting, and class II, partial wetting with thin and thick films; class I, complete wetting, is absent.

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 means of 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 as regards a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. However, a careful FSS analysis of our data favors the field theoretically predicted logarithmic corrections.

The random field Ising model with an asymmetric trimodal probability distribution

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(hi)=pδ(hi−h0)+qδ(hi+h0)+rδ(hi), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), hi is the random field variable and h0 the respective strength. 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 second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0.

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. At 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.

Short-time critical dynamics of the Ising model studied within the N-fold algorithm

The short-time behaviour of the critical two-dimensional Ising model is studied for the Bortz–Kalos–Lebowitz N-fold way algorithm (BKL algorithm). For square lattices of linear sizes L=110,128,140,170, and 200, we calculate the short-time critical behaviour for the BKL algorithm and also for the heat-bath algorithm. Comparison of these results shows that, although power-law scaling form emerges from the early times of the dynamics, there are noticeable differences, which do not produce negligible effects on the estimates of critical exponents. The observed universality of short-time critical behaviour supplements our fundamental knowledge of critical phenomena. However, short-time dynamics seem to be related only approximately with equilibrium critical properties. Therefore, any attempt to estimate equilibrium critical exponents from the short-time regime would be superfluous, except for the purpose of comparison, because these exponents have been determined very precisely by different methods.

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 ρ. 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, ρ 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 h0 increases.

Effective field theory for the Ising model with a fluctuating exchange integral in an asymmetric bimodal random magnetic field: A differential operator technique

The spin-1/2 Ising model on a square lattice, with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field, is investigated within the framework of the effective field theory based on the use of the differential operator relation. The random field is drawn from the asymmetric and anisotropic bimodal probability distribution P(hi)=pδ(hi−h1)+qδ(hi+ch1), where the site probabilities p,q take on values within the interval [0,1] with the constraint p+q=1; hi is the random field variable with strength h1 and c the competition parameter, which is the ratio of the strength of the random magnetic field in the two principal directions +z and −z; c is considered to be positive resulting in competing random fields. The fluctuating bond is drawn from the symmetric but anisotropic bimodal probability distribution P(Jij)=12{δ(Jij−(J+Δ))+δ(Jij−(J−Δ))}, where J and Δ represent the average value and standard deviation of Jij, respectively. We estimate the transition temperatures, phase diagrams (for various values of the system’s parameters c,p,h1,Δ), susceptibility, and equilibrium equation for magnetization, which is solved in order to determine the magnetization profile with respect to T and h1.