Critical effects at 3D wedge wetting

We show that continuous filling transitions are possible in 3D wedge geometries made from substrates exhibiting first-order wetting transitions, and develop a fluctuation theory yielding a complete classification of the critical behavior. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also on an exact transfer-matrix analysis of a novel effective Hamiltonian that we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness xi( perpendicular) approximately (T(F)-T)(-1/4) on approaching the filling temperature T(F), valid for all possible types of intermolecular forces.     

Fluctuation effects on microphase separation in random copolymers

Summary We study random copolymers consisting of two kinds of monomers with attraction between similar kinds. The mean-field analysis of this system indicates a continuous phase transition into a phase with periodic microdomain structure. It is shown that the inverse of the renormalized propagator has a minimum at non-zero wave numbers. Consequently, there is an anomalously large contribution of fluctuations that make the disordered phase locally stable. However, below a certain temperature, the ordered phase is shown to be locally stable and a weak first-order transition is possible, with qualitative differences from the weak crystallization theory developed by Brazovskii. These differences are due to the peculiar form of the fourth-order vertex of the effective Hamiltonian for the system. We calculated the temperature region for the validity of the mean-field estimates of the amplitude and the scale of microphase separation. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

A New First-Order Phase Transition for an Extended Jaynes–Cummings–Dicke Model with a High-Finesse Optical Cavity in the BEC System<Superscript>†</Superscript>

We present a two-level atomic Bose–Einstein condensate (BEC) with dispersion, which is coupled to a high-finesse optical cavity. We call this model the extended Jaynes–Cummings–Dicke (JC-Dicke) model and introduce an effective Hamiltonian for this system. From the direct product of Heisenberg–Weyl (HW) coherent states for the field and U(2) coherent states for the matter, we obtain the potential energy surface of the system. Within the framework of the mean-field approach, we evaluate the variational energy as the expectation value of the Hamiltonian for the considered state. We investigate numerically the quantum phase transition and the Berry phase for this system. We find the influence of the atom–atom interactions on the quantum phase transition point and obtain a new phase transition occurring when the microwave amplitude changes. Furthermore, we observe that the coherent atoms not only shift the phase transition point but also affect the macroscopic excitations in the superradiant phase.     

Phase transitions, interfacial fluctuations and hidden symmetries for fluids near structured walls

Fluids adsorbed at micro-patterned and geometrically structured substrates can exhibit novel phase transitions and interfacial fluctuation effects distinct from those characteristic of wetting at planar, homogeneous walls. We review recent theoretical progress in this area paying particular attention to filling transitions pertinent to fluid adsorption near wedges, which have highlighted a deep connection between geometrical and contact angles. We show that filling transitions are not only characterized by large scale interfacial fluctuations leading to universal critical singularities but also reveal hidden symmetries with short-ranged critical wetting transitions and properties of dimensional reduction. We propose a non-local interfacial model which fulfills all these properties and throws light on long-standing problems regarding the order of the 3D short-range critical wetting transition.     

Tetra point wetting at the free surface of liquid Ga-Bi

A continuous surface wetting transition, pinned to a solid-liquid-liquid-vapor tetra coexistence point, is studied by x-ray reflectivity in liquid Ga-Bi binary alloys. The short-range surface potential is determined from the measured temperature evolution of the wetting film. The thermal fluctuations are shown to be insufficient to induce a noticeable breakdown of mean-field behavior, expected in short-range-interacting systems due to their d(u) = 3 upper critical dimensionality.     

The capillary-wave Hamiltonian for an interface in the presence of a weakly corrugated substrate

We derive within the mean-field version of the Landau-Ginzburg -Wilson theory the expression for the capillary-wave Hamiltonian of the interface between twophases of an uniaxial ferromagnet fluctuating in the presence of a weakly corrugated, asymptotically flat substrate. The coefficients of interfacial stiffness as well as the coefficient multiplying the coupling between the ondulations of the interface and the corrugation of the substrate are shown to depend on the local distance l between the interface and the substrate. This distance dependence goes via the exponentially decaying terms which are multiplied by polynomials in l. Using this capillary-wave Hamiltonian we show that the weak corrugation of the substrate does not lead to a shift of the critical wetting temperature as compared to the flat substrate case.     

Density fluctuations in the presence of spinodal instabilities

Density fluctuations resulting from spinodal decomposition in a nonequilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first-order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to the Nambu-Jona-Lasinio model formulated at finite temperature and density. However, our main conclusions are expected to be generic and model independent.     

Free-Energy Bounds for Hierarchical Spin Models

In this paper we study two non-mean-field (NMF) spin models built on a hierarchical lattice: the hierarchical Edward–Anderson model (HEA) of a spin glass, and Dyson’s hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence of the thermodynamic limit of the free energy and the replica-symmetry-breaking (RSB) free-energy bounds previously derived for the Sherrington–Kirkpatrick model of a spin glass. These RSB mean-field bounds are exact only if the order-parameter fluctuations (OPF) vanish: given that such fluctuations are not negligible in NMF models, we develop a novel strategy to tackle part of OPF in hierarchical models. The method is based on absorbing part of OPF of a block of spins into an effective Hamiltonian of the underlying spin blocks. We illustrate this method for DHM and show that, compared to the mean-field bound for the free energy, it provides a tighter NMF bound, with a critical temperature closer to the exact one. To extend this method to the HEA model, a suitable generalization of Griffith’s correlation inequalities for Ising ferromagnets is needed: since correlation inequalities for spin glasses are still an open topic, we leave the extension of this method to hierarchical spin glasses as a future perspective.     

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.     

Space Dependent Mean Field Approximation Modelling

It is shown that the self-consistency condition which is the basic equation for calculating the mean-field order parameter of any mean-field model Hamiltonian can be replaced by the standard Metropolis Monte Carlo scheme. The advantage of this method is its ease of implementation for both the homogeneous mean-field order parameter and the heterogeneous one. To be specific, the mean-field version of the Ising model spin system is discussed in detail and the resulting magnetization is the same as in the case of solving the respective mean-field self-consistency equation. In addition, it is shown that if a high temperature phase of such system is quenched below critical temperature then the mean field experienced by spins develops into a network of domains in analogous way as it happens with the spins in the case of the exact many-body Hamiltonian system and the coarsening processes start to take place. To show that the introduced Metropolis Monte Carlo method works also in case of the continuous variables the order parameter for the Maier-Saupe model for nematic liquid crystals has been calculated.     

3D short-range wetting and nonlocality

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.     

Nonlocality and short-range wetting phenomena

We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.     

Coexistence of ferromagnetism and superconductivity close to a quantum phase transition: the Heisenberg- to Ising-type crossover

A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transition is analyzed and the generic phase diagram is obtained. This scenario is then applied to the case of itinerant ferromagnet ZrZn2, which sheds light on the proposed phase diagram of this compound. A possible explanation of superconductivity in UGe2 is also discussed.     

Influence of disorder on the magnetism of graphene bilayers

We numerically calculate the impact of site-energy disorder on the magnetism of biased bilayer graphene formed with the Bernal stacking. By using the mean-field method, we approximately solve the Hubbard Hamiltonian and calculate the average magnetization of the two layers, which indicates that the disorder does not change the nature of the first-order phase transition between paramagnetism and ferromagnetism, but may increase the critical interaction strength U_c of the Hubbard Hamiltonian for the system to become the ferromagnetic phase. We also calculate the dependencies of relevant physical quantities on temperature. The implications of the results are discussed.     

Squeezing States of Magnons in a Ferromagnet

In this paper, we conduct an investigation into magnon self-squeezing states in a ferromagnet. In these states, the quantum fluctuations of the spin components can be lower than the zero-point quantum fluctuations of the coherent states. Through calculating the expectation values of spin fluctuations we gain the condition of achieving magnon self-squeezing. We introduce the mean-field theory for dealing with the nonlinear interaction term of Hamiltonian of magnon system.     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

Core-halo distribution in the Hamiltonian mean-field model

We study a paradigmatic system with long-range interactions: the Hamiltonian mean-field (HMF) model. It is shown that in the thermodynamic limit this model does not relax to the usual equilibrium Maxwell-Boltzmann distribution. Instead, the final stationary state has a peculiar core-halo structure. In the thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find that using dynamical properties of Hamiltonian systems it is possible to quantitatively predict both the spin distribution and the velocity distribution functions in the final stationary state, without any adjustable parameters. We also show that HMF undergoes a nonequilibrium first-order phase transition between paramagnetic and ferromagnetic states.     

Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka–Volterra type interactions defined on a d-dimensional lattice. Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical, deterministic mean-field picture. Already within mean-field theory, however, spatial constraints, modeling locally limited resources, lead to the emergence of a continuous active-to-absorbing state phase transition. Field-theoretic arguments, supported by Monte Carlo simulation results, indicate that this transition, which represents an extinction threshold for the predator population, is governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical center singularities with associated population cycles are replaced by either nodes or foci. In the vicinity of the stable nodes, the system is characterized by essentially stationary localized clusters of predators in a sea of prey. Near the stable foci, however, the stochastic lattice Lotka–Volterra system displays complex, correlated spatio-temporal patterns of competing activity fronts. Correspondingly, the population densities in our numerical simulations turn out to oscillate irregularly in time, with amplitudes that tend to zero in the thermodynamic limit. Yet in finite systems these oscillatory fluctuations are quite persistent, and their features are determined by the intrinsic interaction rates rather than the initial conditions. We emphasize the robustness of this scenario with respect to various model perturbations.     

Mean-field phenomenology of wetting in nanogrooves

ABSTRACT

In this special issue article, we bring together our recent research on wetting in confinement, in particular planar walls, wedges, capillary grooves and slit pores, with emphasis on phase transitions and competition between wetting, filling and condensation, and highlight their similarities and disparities. The results presented are obtained with the classical density functional theory (DFT) for fluids, which is a mean-field statistical mechanical framework for including the spatial variations of the fluid density into the thermodynamic equation of state. For wetting in sculpted substrates, we solve numerically the DFT equations to obtain the fluid density profiles, wetting isotherms and phase diagrams. This allows us to contrast the wetting phenomenology of grooves, planar walls, slit and wedge-shaped pores. Of particular interest are the transitions associated with capillary condensation, planar pre-wetting and mean-field wedge pre-filling lines.