The existence of a phase transition in classical antiferromagnetic models

For a wide class of antiferromagnetic models we prove the existence of a phase transition using an extended Peierls argument, taking into account a result of Dobrushin [R. L. Dobrushin,Funct. Anal. Appl. 2:44 (1968); in English,2:302 (1968)] for an antiferromagnetic Ising model and the results of Malyshev [V. Malyshev,Comm. Math. Phys. 40:75–82 (1975)] for ferromagnetic models (such as the anisotropic rotator). In particular we review a result of Fröhlich, Israel, Lieb, and Simon [J. Fröhlichet al., J. Stat. Phys. 22(3):297–347 (198)] obtained when reflection positivity holds.     

Polymer mixtures in confined geometries: Model systems to explore phase transitions

While binary (A,B) symmetric polymer mixtures ind = 3 dimensions have an unmixing critical point that belongs to the 3d Ising universality class and crosses over to mean field behavior for very long chains, the critical behavior of mixtures confined into thin film geometry falls in the 2d Ising class irrespective of chain length. The critical temperature always scales linearly with chain length, except for strictly two-dimensional chains confined to a plane, for whichT _c ∝N ^5/8 (this unusual exponent describes the fractal contact line between segregated chains in dense melts in two spatial dimensions,d = 2). When the walls of the thin film are not neutral, but preferentially attract one species, complex phase diagrams occur due to the interplay between capillary condensation and wetting phenomena. For ‘competing walls’ (one wall prefers A, the other prefers B) particularly interesting interface localization-delocalization transitions occur, while analogous phenomena in wedges are related to the ‘filling transition’.     

Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices

We study the critical behavior of the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices. We compare our results obtained by three different numerical methods namely the multifractal analysis, the Green resolvent method, and the energy-level statistics which yield the singularity strength, the decay length of the wave functions, and the (integrated) energy-level distribution, respectively. From these measures a finite-size scaling approach allows us to determine the critical parameters simultaneously. With particular emphasis we calculate the propagation of the statistical errors by a Monte-Carlo method. We find a high agreement between the results of all methods and we can estimate the highest critical disorder W _c = 14.474 (8) at energy E _c = ? 4.0 and the critical exponent ν = 1.565 (11). Our results agree with a previous study by Fazileh et al. [F. Fazileh, X. Chen, R.J. Gooding, K. Tabunshchyk, Phys. Rev. B 73, 035124 (2006)] but improve accuracy significantly.     

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.     

Nature of asymmetry in fluid criticality

By combining accurate liquid-vapor coexistence and heat-capacity data, we have unambiguously separated two nonanalytical contributions of liquid-gas asymmetry in fluid criticality and showed the validity of "complete scaling" [Fisher, Phys. Rev. Lett. 85, 696 (2000)10.1103/PhysRevLett.85.696; Phys. Rev. E 67, 061506 (2003)10.1103/PhysRevE.67.061506]. We have also developed a method to obtain two scaling-field coefficients, responsible for the two sources of the asymmetry, from mean-field equations of state. Since the asymmetry effects are completely determined by Ising critical exponents, there is no practical need for a special renormalization-group theoretical treatment of asymmetric fluid criticality.     

Morphology and structure of thin liquid-crystalline films at nematic-isotropic transition

We review the main features of very thin nematic liquid-crystalline films on solid substrates, focusing on 5CB on oxidized silicon wafers. By discussing the theoretical aspects of the observed structures, we show that the phenomena at work include isotropic capillary condensation and that the coexistence of isotropic and nematic terraces in thin films is a result of the interplay of several mechanisms. Further theoretical as well as experimental efforts are needed to completely understand the wetting behavior of these systems.Received: 1 August 2003PACS: 68.08.Bc Wetting - 68.15. + e Liquid thin films - 61.30.Hn Surface phenomena in liquid crystals including anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions     

Corner wetting in a far-from-equilibrium magnetic growth model

The irreversible growth of magnetic films is studied in three-dimensional confined geometries of size L×L×M, where M≫L is the growing direction. Competing surface magnetic fields, applied to opposite corners of the growing system, lead to the observation of a localization-delocalization (weakly rounded) transition of the interface between domains of up and down spins on the planes transverse to the growing direction. This effective transition is the precursor of a true far-from-equilibrium corner wetting transition that takes place in the thermodynamic limit. The phenomenon is characterized quantitatively by drawing a magnetic field-temperature phase diagram, firstly for a confined sample of finite size, and then by extrapolating results, obtained with samples of different size, to the thermodynamic limit. The results of this work are a nonequilibrium realization of analogous phenomena recently investigated in equilibrium systems, such as corner wetting transitions in the Ising model.     

Spurious character of singularities associated with phase transitions in cylindrical pores

Phase transitions of simple fluids and binary fluid mixtures confined into long cylindrical pores are re-examined, such as capillary condensation/evaporation and wetting transitions. While a large part of the literature ignores the fact that due to the quasi-one-dimensional character of these systems a singular behavior associated with a sharp phase transition cannot occur, we pay attention to the extent in which these phase transitions are smoothed out (in relation to the magnitude of the pore cross-sectional area). We argue that the finiteness of the pore length is an important parameter which controls the physical phenomena that are observed in simulations (and presumably also experiments explaining the distinction between the apparent “pore critical temperature” and the “hysteresis critical temperature”). We illustrate our arguments with recent findings from simulations of a lattice gas/Ising system and of the Asakura-Oosawa model of colloid-polymer mixtures.     

Condensation in a capped capillary is a continuous critical phenomenon

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions, the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively, and are equivalent to 2D-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In two dimensions we establish precise connection, or covariance, with 2D critical-wetting and wedge-filling transitions: i.e., we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in two and three dimensions.     

Low-temperature nucleation in a kinetic Ising model with soft stochastic dynamics

We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, =Aexp((betagamma) (beta=1/k(B)T) [Commun. Math. Phys. 137, 209 (1991)]]. Contrary to common belief, we find that both A and Gamma depend significantly on the stochastic dynamic. In particular, for a "soft" dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Gamma does not simply equal the energy barrier against nucleation, as it does for the standard Glauber dynamic, which does not have this factorization property.     

Monte Carlo methods for the study of phase transitions and phase equilibria

Monte Carlo methods can predict macroscopic properties of N-body systems from the (classical) Hamiltonian describing the interactions between the particles and hence can serve as a basic tool of equilibrium statistical mechanics, avoiding uncontrolled approximations. However, a necessary ingredientis the control of finite size effects. For this purpose, the finite size scaling analysis of suitable distribution functions is a powerful tool. The basic ideas of this approach will be discussed, including extensions to critical phenomena where the hyperscaling relation between critical exponents is violated (colloid-polymer mixtures in random media as a realization of the random field Ising model, phase transitions caused by competition of interfacial and surface effects, etc.) Finite size effects on two-phase coexistence cause the existence of a van-der-Waals-like loop, but it has a completely different origin, the “spinodal” reflecting the “droplet evaporation/condensation” transition. Also the possibility to extract interface free energies is discussed.     

Ising Critical Exponents on Random Trees and Graphs

We study the critical behavior of the ferromagnetic Ising model on random trees as well as so-called locally tree-like random graphs. We pay special attention to trees and graphs with a power-law offspring or degree distribution whose tail behavior is characterized by its power-law exponent τ > 2. We show that the critical inverse temperature of the Ising model equals the hyperbolic arctangent of the reciprocal of the mean offspring or mean forward degree distribution. In particular, the critical inverse temperature equals zero when ${\tau \in (2,3]}$ where this mean equals infinity. We further study the critical exponents δ, β and γ, describing how the (root) magnetization behaves close to criticality. We rigorously identify these critical exponents and show that they take the values as predicted by Dorogovstev et al. (Phys Rev E 66:016104, 2002) and Leone et al. (Eur Phys J B 28:191–197, 2002). These values depend on the power-law exponent τ, taking the same values as the mean-field Curie-Weiss model (Exactly solved models in statistical mechanics, Academic Press, London, 1982) for τ > 5, but different values for ${\tau \in (3,5)}$ .     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

Helium wetting: Theme and variations on inhomogeneous helium

The surprising discovery, in 1991, that liquid helium does not wet a cesium surface at low temperature has triggered an important activity both theoretical and experimental: helium has become a model system for the study of wetting transitions. After summarizing the main theme of helium wetting, I will focus on more recent studies, such as the structure and excitations of helium interfaces, experiments on the capillary rise, the “surfactant effect” of helium-3 impurities on liquid helium-4 and the “quantum prewetting transition” of pure helium-3. Unexpected consequences on the phase separation of³He?⁴He mixtures in restricted geometry will be drawn.     

On the phase boundaries of the integer quantum hall effect

It has been pointed out that, according to the two-parameter scaling theory, the magnetic-field position of the phases of the integer quantum Hall effect (IQHE) at ω_cτ ? 1 is not determined by the filling factor ν = nh/eB. The position of the IQHE phases is given by the bare Hall conductivity σ _xy ⁰ . In this regard, it has been shown that the diagonal resistivity in the magnetic field measured by Sakr et al. [Phys. Rev. B 64, 161308 (2001)] does not exhibit transitions between the σ _xy = 3, 4 and 6 IQHE states on the one hand and the dielectric state on the other hand in contrast to the assertion by Sakr et al.     

Non-integrable quantum field theories as perturbations of certain integrable models

We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and form factors of the integrable field theories we obtain the first-order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T_c and the scaling region around the minimal model M_2,7. For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalisation of their Hamiltonian.     

First-principles simulations for attosecond photoelectron spectroscopy based on time-dependent density functional theory

We develop a first-principles simulation method for attosecond time-resolved photoelectron spectroscopy. This method enables us to directly simulate the whole experimental processes, including excitation, emission and detection on equal footing. To examine the performance of the method, we use it to compute the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) experiments of gas-phase Argon. The computed RABBITT photoionization delay is in very good agreement with recent experimental results from [Klünder et al., Phys. Rev. Lett. 106, 143002 (2011)] and [Guénot et al., Phys. Rev. A 85, 053424 (2012)]. This indicates the significance of a fully-consistent theoretical treatment of the whole measurement process to properly describe experimental observables in attosecond photoelectron spectroscopy. The present framework opens the path to unravel the microscopic processes underlying RABBITT spectra in more complex materials and nanostructures.     

Slow Dynamics for the Dilute Ising Model in the Phase Coexistence Region

In this paper we consider the Glauber dynamics for a disordered ferromagnetic Ising model, in the region of phase coexistence. It was conjectured several decades ago that the spin autocorrelation decays as a negative power of time [Huse and Fisher, in Phys Rev B 35(13):6841–6846, 1987]. We confirm this behavior by establishing a corresponding lower bound in any dimensions d ≥ 2, together with an upper bound when d = 2. Our approach is deeply connected to the Wulff construction for the dilute Ising model. We consider initial phase profiles with a reduced surface tension on their boundary and prove that, under mild conditions, those profiles are separated from the (equilibrium) pure plus phase by an energy barrier.     

Critical behavior of the two-dimensional thermalized bond Ising model

A suitably modified Wolff single-cluster Monte Carlo simulation has been performed to investigate the critical behavior of a two-dimensional Ising model with temperature-dependent annealed bond dilution, also known as the thermalized bond Ising model, which is intended to simulate the thermal excitations of electronic bond degrees of freedom as in covalently bonded network liquids. A finite-size scaling analysis of the susceptibility and the fourth-order cumulant, results in a reliable estimation of the critical exponents in the thermodynamic limit. The exponents are found to be consistent with those predicted by the Fisher renormalization relations, despite the well known violations of the renormalization relations when approximate methods such as real space renormalization group are employed to investigate two-dimensional Ising model with annealed bond dilution, and the temperature variation of the bond concentration in thermalized bond model system.     

Critical behavior of geometric measure of quantum discord when approaching the critical points via different paths

We investigate the critical behavior of geometric measure of quantum discord (GMQD) in a one-dimensional transverse XY spin chain. The critical and the scaling behavior of the ground state GMQD are investigated both at the multi-critical and Ising critical points. Our results show that the behavior of GMQD at muti-critical point (MCP) has close relation with the path, which is determined by the parameter α, that approaching the MCP. For α < 2, the GMQD and its first derivation show oscillation behavior. For α ≥ 2, no oscillation behavior is observed. This indicates that the GMQD can not describe exactly the multi-critical point of the XY model. However, at the Ising critical point, the path parameter has no influence on the critical behavior. The GMQD (first derivation of GMQD) shows peaks (dips) and indicates exactly the position of Ising critical point. The results also show that the path parameter influences much to the scaling behavior near the MCP, but less to that of Ising critical point. Our results may provide reference to the exploration of relationships between GMQD and quantum phase transitions.