Ising Films Research Articles

Solvation forces in Ising films with long-range boundary fields: density-matrix renormalization-group study

Using the quasi-exact density-matrix renormalization-group method we calculate the solvation forces in two-dimensional Ising films of thickness L subject to identical algebraically decaying boundary fields with various decay exponents p. At the bulk critical point the solvation force acquires a universal contribution which is long-ranged in L due to the critical fluctuations, a phenomenon known as the critical Casimir effect. For p = 2, 3 and 50, we study the scaling behaviour of the solvation force along the pseudo-phase coexistence and along the critical and sub-critical isotherms.

Crossover of critical Casimir forces between different surface universality classes

In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean-field theory. Within our approach, the scaling functions of the critical Casimir force and of the order parameter profile for finite surface fields can be mapped by rescaling, except for a narrow crossover regime, onto the corresponding scaling function of the so-called normal fixed point of strong surface fields. In the crossover regime, the critical Casimir force as function of temperature exhibits more than one extremum and for certain ranges of surface field strengths it changes sign twice upon varying temperature. Monte Carlo simulation data obtained for a three-dimensional Ising film show similar trends. The sign of the critical Casimir force can be inferred from the comparison of the order parameter profiles in the film and in the semi-infinite geometry.

Magnetic phase transition in antiferromagnetic films

The susceptibility of body-centered cubic lattice (bcc) antiferromagnetic spin- 1 2 through two model: Ising and XY films consisting of n = 2 , 3 , 4 , 5 , and 6 interacting layers is studied by high-temperature series expansions. Sixth order series in x = β J ( β = 1 k B T ) have been obtained for free-surface boundary conditions. The high temperature series expansion of the magnetic susceptibility series has been investigated by using the Padé approximant method. The Néel temperatures T N ( n ) as a function of the number of n spin layers in the films is obtained. The critical exponent γ associated with the magnetic susceptibility is deduced for Ising and XY models. The shifts of the critical temperatures from the bulk value [ T N ( ∞ ) T N ( n ) − 1 ] can be described by a power law n − λ with λ = 1 ν , where ν is the correlation length exponent.

Phase Coexistence in Nanoscopically Thin Films Confined by Asymmetric Walls

Thin Ising films with nearest-neighbor ferromagnetic exchange in a bulk magnetic field H are studied in a L×L×D geometry, where at the opposite walls, given by the L×L surfaces, local magnetic fields H1, and HD act. While in previous work, the symmetric case H1=HD (leading to “capillary condensation”, when one applies the lattice gas terminology) as well as the antisymmetric case H1=−HD (leading to “interface localization transitions”) were studied, we focus here on the general ‘asymmetric’ case. Monte Carlo simulations are carried out and analyses based on thermodynamic integration methods are used to establish the phase diagrams and study the properties of the coexisting phases. A discussion is given why for the range of thicknesses that is explored (16≤D≤80 lattice spacings) this is the most suitable methodology. Restricting attention to cases where in the semi-infinite system a first-order wetting transition occurs, it is shown that the latter, due to confinement, is turned in a thin-film triple point. Above the triple point, narrow two-phase coexistence curves are found, which are the analog of prewetting transitions in the semi-infinite system. A comparison to related results for (symmetrical) polymer blends and (asymmetric) colloid-polymer mixtures is made.

Spin-1/2 Ising Films with a Non Perfect Surface

The influence of a non-perfect surface on the critical properties of magnetic spin-1/2 Ising film on a cubic lattice structure is studied using Monte Carlo simulations based on Metropolis algorithm. The surface magnetization and the surface effective exponent have been studied for several concentration p. Far from the critical temperature, the surface effective exponent βeff s decreases with increasing the concentration p.

Monte Carlo Study of Spin-1/2 Ising Thin-Films

Using Monte Carlo simulation with the Metropolis algorithm, we have studied the critical behaviour of magnetic spin 1/2 Ising film on a cubic lattice structure. We drive the effective exponent of the each layer βeff(z,t) and of the film βeff f (t) as a function of reduced temperature t. A particular attention is paid for the evaluation of the variation of the critical exponents with the film thickness.

Phase Transition and Magnetic Properties of a Decorated Ising Film

The magnetic properties and the phase diagrams of a decorated Ising film on the cubic lattice are investigated within the framework of an effective field theory based on the use of a probability distribution technique. The system studied consists of two magnetic atoms species A and B with σA = 1/2 and SB = 1, where the B sites decorate the bonds between A sites. The effect of the crystal field and the thickness of the film, on the behaviour of the system, are examined. We find a number of characteristic phenomena such as the possibility of two compensation points and the double reentrant phenomenon.

Phase transition and magnetic properties of a decorated Ising film: Monte Carlo and effective field treatments

A Monte Carlo Simulation (MCS) has been used to study critical behavior and magnetic properties of a decorated Ising film on a cubic lattice structure. The system consists of two magnetic atoms species A and B with σ A = 1 / 2 and S B = 1 , where the B sites decorate the bonds between A sites. The dependence of the phase diagram on the axial zero-field splitting parameter, the exchange interactions and the thickness of the film are studied. We found that the system exhibits a double reentrant phenomenon and one or two compensation points. MCS results are compared to those obtained by using the effective field theory (EFT) based on the use of a probability distribution technique. However, MCS predicts the same topology of the phase diagrams as the effective field theory.

Monte Carlo study of the spin-1 Blume–Capel Ising film

Using Monte Carlo simulations with the Metropolis algorithm, we have studied the influence of crystal-field interaction on the critical behavior of magnetic spin-1 Ising film on a cubic lattice structure. The phase diagrams in the ( k B T c / J , R = J s / J ) plane are obtained for different values of the crystal-field interaction. We found that the special point R sp ( R c ) , at which the critical temperature is independent of the film thickness N, is independent of the crystal-field interaction and that the system may exhibit a tricritical behavior.

Dynamical behavior of three-dimensional confined Ising systems with short- and long-range competing surface fields

The dynamical behavior of ferromagnetic Ising films confined in a DxLxL geometry (D<<L,1< or =i< or =D) is studied by means of Monte Carlo simulations when either short- or long-range competing magnetic fields H(i) of equal strength but opposite sign are applied at opposite walls, given by the LxL surfaces. It is well known that, for appropriate choices of the control parameters, these systems exhibit wetting phase transitions that occur in the limit of infinite film thickness at the critical curve Tw(hw) , where hw=H(i=1) is the magnitude of the surface field at the wall. Results of the dynamical approach to equilibrium, at criticality and for the complete wetting regime, obtained by starting the systems from different (far-from equilibrium) initial conditions, are presented and discussed. We determine quite accurately a wetting critical point [Tw=0.8982(57),hw=0.555] for the case of short-range fields, by measuring the detachment of the wetting layer from a wall, which for this type of field obeys a logarithmic dependence on time. For retarded van der Waals forces we obtained [Tw=0.8982,hw=0.449(1)] for the critical point. The scaling behavior of the average position of the interface is also studied for the complete wetting regime at T=0.8982 and in the presence of a bulk magnetic field H=1 . The numerical results are in full agreement with the theoretical expectations for the cases of short-range and long-range (both retarded and nonretarded van der Waals forces) fields, where logarithmic and power-law divergences are found, respectively.

The spin- [formula omitted] Ising film with surface defects

Using Monte Carlo simulations, we have studied the influence of surface defects on the critical behavior of magnetic spin- 1 2 Ising film on a cubic lattice structure. We derive the phase diagram and the critical exponent β in the case of a perfect surface. In such films, the critical temperature can shift to either lower or higher values compared to the corresponding bulk one. In the case of a surface with random, ‘weak’ or ‘strong’ interactions between neighboring spins, it is found that the critical exponent β 1 follows very closely that of the perfect surface case. Far from the critical temperature, the effective exponent decreases with increasing the concentration of strong interactions p.

The spin-1/2 Ising film with a perfect surface

The critical properties of the magnetic spin-1/2 Ising film are studied using the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions. We discuss an L-layer film of simple cubic symmetry with nearest-neighbour interactions in which the strength of the interaction at the surface is different from the bulk value. We derive the phase diagram, the longitudinal susceptibility and the effective critical exponents in the case of a perfect surface. In such films, the critical temperature can shift to either lower or higher temperature compared to the corresponding bulk value.

Study of the confined Ising magnet with long-range competing boundary fields

We present extensive Monte Carlo simulations of the Ising film confined in anL × M geometry () in the presence of long-range competing magnetic fieldsh(n) = h1/n3(n = 1,2,...,L) which are applied at opposite walls along theM-direction. Due to the fields, an interface between domains of different orientations thatruns parallel to the walls forms and can be located close to one of the two surfaces orfluctuate in the centre of the film (localization–delocalization transition). This transition isthe precursor of the wetting phase transition that occurs in the limit of infinite filmthickness () at the critical curve Tw(h1). For T<Tw(h1) (T≥Tw(h1)) such an interface is bound to (unbound from) the walls.We study this transition by measuring the magnetization profiles across thesample and the distribution function of both the magnetization of the wholesample and that of the centre of the film as a function of temperature,T, or strength ofthe wall field, h1. We obtain estimates of the size-dependent wetting ‘critical’ points that allow us toextrapolate to the thermodynamic limit. Using the results of these extrapolations,confirmed by independent measurements of the cumulant, we draw the phase diagram ofthe wetting transition with long-range surface fields.We show that, starting from a localized interface well inside the non-wet phase, theposition of the interface diverges exponentially when approaching the transition point, incontrast to the power-law divergence observed in the case of short-range fields.The properties of the delocalized interface are also studied. Within the wet phase the widthof the capillary waves broadens the observed interface profiles. The spectrum of capillarywaves is cut off at large wavelengths by the correlation length, , which scales like , similar to the short-range case. Additionally, the interface stiffness is obtained from theFourier spectrum of the capillary waves.

The order parameter and critical behavior of the spin [formula omitted] Ising film

Using the effective field theory with a probability distribution technique that accounts for the self-spin correlations, we have studied the influence of surface defects on the critical properties of the magnetic spin Ising film. We discuss an L layer film of simple cubic symmetry with nearest-neighbor interactions in which the strengths of the interactions at the surfaces are different from the bulk value. We derive the phase diagram, the longitudinal susceptibility and the effective critical exponent in the case of perfect surface. In such films, the critical temperature can shift to either lower or higher temperature compared to the corresponding bulk value. In the case of surface with random interaction, it is found that the critical exponent β 1 follows very closely that of the perfect surface case, and far from the critical temperature, the effective exponent decreases with increasing the concentration p.

Effects of spin–phonon interaction on the dynamical properties of thin ferroelectricfilms

The effects of spin–phonon interaction on the temperature dependence of the spin-wave andphonon spectrum in thin ferroelectric transverse Ising films are studied using aGreen function formalism beyond the random phase approximation. It is shownthat due to the surface modes and the spin–phonon interaction the spin-wavedamping effects in thin ferroelectric films are enhanced in comparison to thebulk. The phonon spectrum is discussed, too. Additional phonon damping andphonon frequency shift arise when the spin–phonon interaction is properly included.

First-order interface localization-delocalization transition in thin Ising films using Wang-Landau sampling

Using extensive Monte Carlo simulations, we study the interface localization-delocalization transition of a thin Ising film with antisymmetric competing walls for a set of parameters where the transition is strongly first order. This is achieved by estimating the density of states (DOS) of the model by means of Wang-Landau sampling (WLS) in the space of energy, using both single-spin-flip as well as N-fold way updates. From the DOS we calculate canonical averages related to the configurational energy, like the internal energy and the specific heat, as well as the free energy and the entropy. By sampling micro-canonical averages during simulations we also compute thermodynamic quantities related to magnetization like the reduced fourth-order cumulant of the order parameter. We estimate the triple temperatures of infinitely large systems for three different film thicknesses via finite size scaling of the positions of the maxima of the specific heat, the minima of the cumulant, and the equal weight criterion for the energy probability distribution. The wetting temperature of the semi-infinite system is computed with help of the Young equation. In the limit of large film thicknesses the triple temperatures are seen to converge toward the wetting temperature of the corresponding semi-infinite Ising model in accordance with standard capillary wave theory. We discuss the slowing down of WLS in energy space as observed for the larger film thicknesses and lateral linear dimensions. In the case of WLS in the space of total magnetization we find evidence that the slowing down is reduced and can be attributed to persisting free energy barriers due to shape transitions.

Critical Casimir Effect in Three-Dimensional Ising Systems: Measurements on Binary Wetting Films

The critical Casimir force (CF) is observed in thin wetting films of a binary liquid mixture close to the liquid/vapor coexistence. X-ray reflectivity shows thickness (L) enhancement near the bulk consolute point. The extracted Casimir amplitude Delta(+-)=3+/-1 agrees with the theoretical universal value for the antisymmetric 3D Ising films. The onset of CF in the one-phase region occurs at L/xi approximately 5 regardless of whether the bulk correlation length xi is varied with temperature or composition. The shape of the Casimir scaling function depends monotonically on the dimensionality.

Interfaces in the confined Ising system with competing surface fields

When a magnetic Ising film is confined in a L × M geometry ( L ⪡ M ) short-range competing magnetic fields ( h 1 ) are applied at opposite walls along the M -direction, a (weakly rounded) localization–delocalization transition of the interface between domains of different orientation that runs parallel to walls can be observed. This transition is the precursor of a wetting phase transition that occurs in the limit of infinite film thickness ( L → ∞ ) at the critical curve T w ( h 1 ) . For T < T w ( h 1 ) ( T > T w ( h 1 ) ) such an interface is bound to (unbound from) the walls, while right at T w ( h 1 ) the interface is freely fluctuating around the center of the film. We present extensive Monte Carlo simulations of Ising stripes in the L × M geometry, in order to describe both the localization–delocalization transition and the properties of the delocalized interface. To this aim, we take advantage of several available theoretical results. We make use of a suitable algorithm to define the local position of the interface along the film, such that its probability distribution can be used to account for the transition itself and the fluctuations in the local position of the interface (capillary waves). After describing the interface localization–delocalization transition, we pay attention to the properties of the delocalized interface with an emphasis on the effects of confinement. We analyze several quantities of interest in terms of the film thickness L . The width of the capillary waves ( s ) can be related to the width of the magnetization profiles ( w ) by means of a simple approximation. From this relation we estimate a value for the intrinsic width ( w 0 ) of the interface which agrees with the theoretical one. Also the correlation length ξ ∥ along the film is considered, and the behavior ξ ∥ ∼ L 2 compares very well to available exact results. Additionally, the interfacial stiffness β Γ obtained from the Fourier spectrum of the capillary waves reproduces the asymptotic theoretical value.

Green's function theory for a magnetic impurity layer in a ferromagnetic Ising film with transverse field

A Green's function formalism is used to calculate the spectrum of localized modes of an impurity layer implanted within a ferromagnetic thin film. The equations of motion for the Green's functions are determined in the framework of the Ising model in a transverse field. We show that depending on the thickness, exchange and effective field parameters, there is a “crossover” effect between the surface modes and impurity localized modes. For thicker films the results show that the degeneracy of the surface modes can be lifted by the presence of an impurity layer.

Study of the dynamical approach to the interface localization–delocalization transition ofthe confined Ising model

Confined magnetic Ising films in aL × D geometry (), with short-range competing magneticfields (h) acting atopposite walls along the D-direction, exhibit a slightly rounded localization–delocalization transition of the interfacebetween domains of different orientations that runs parallel to the walls. This transition isthe precursor of a wetting transition that occurs in the limit of infinite film thickness () at the critical curve Tw(h). For T<Tw(h) (T>Tw(h)) such an interface is bounded (unbounded) to the walls, while right atTw(h) the interface is freely fluctuating around the centre of the film.Starting from disordered configurations, corresponding to , we quench to the wetting critical temperature and study the dynamics of the approach tothe stationary regime by means of extensive Monte Carlo simulations. It is found that forall layers parallel to the wall (rows), the row magnetizations exhibit a peak at a time and subsequently relax to the stationary, equilibrium behaviour. The characteristic timefor such a relaxation scales as , as expected from theoretical arguments, that are discussed in detail.