Unbinding transitions of membranes and strings from single and double-well potential

We present a theory of unbinding transitions for membranes that interact via short and long receptor/ligand bonds. The detail of unbinding behaviour of the membranes is governed by the binding energies and concentrations of receptors and ligands. We investigate the unbinding behaviour of these membranes with Monte Carlo simulations and via a comparison with strings. We derive the scaling laws for strings analytically. The exact analytical results provide scaling estimate for membranes in the vicinity of the critical point.     

Strings in charge-transfer Mott insulators: Effects of lattice vibrations and the Coulomb interaction

Applying the canonical transformation with the 1/λ perturbation expansion in the nonadiabatic and intermediate regime and the discrete generalization of Pekar’s continuous nonlinear equation in the extreme adiabatic regime, we show that there are no strings in narrow-band ionic insulators due to the Fröhlich electron-phonon interaction alone. The multipolaron system is a homogeneous state in a wide range of physically interesting parameters, no matter how strong the correlations are. At the same time, the Fröhlich interaction allows the antiferromagnetic interactions and/or short-range electron-phonon interactions to form short strings in doped antiferromagnetic insulators if the static dielectric constant is large enough.     

Deconfinement in the two-dimensional XY model

The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system supports two phase transitions, one in which closed strings proliferate, and a second in which vortices unbind. The transitions are shown to be dual to one another, and are remarkably continuous. Possible consequences for a variety of systems are discussed.     

Phase transitions for two-dimensional models with isotropic short-range interactions and continuous symmetries

Using the powerful method of reflection-positivity and chess-board estimates, we prove the existence of phase transition for certain class of isotropic short-range interactions with continuous symmetry, provided that the dimension of the lattice is at least two, and the temperature is low enough.     

Helfrich repulsion and dynamical phase separation of multicomponent lipid bilayers

Thermal fluctuations of surfactant bilayers in an aqueous solution produce an effective, long-range repulsion that can lead to a continuous unbinding transition. We report on an optical interferometry study of the thermal fluctuations of multicomponent bilayers close to the unbinding transition. We find that, in contrast to the case of single-component bilayers, the thermal fluctuation spectrum of multicomponent bilayers does not agree with a continuous unbinding transition but instead indicates the proximity of an unbinding tricritical point.     

Discontinuous unbinding of lipid multibilayers

We have observed a discontinuous unbinding transition of lipid bilayer stacks composed of phosphatidylethanolamine and phosphatidylglycerol using x-ray diffraction. The unbinding is reversible and coincides with the main (L(beta)-->L(alpha)) transition of the lipid mixture. Interbilayer interaction potentials deduced from the diffraction data reveal that the bilayers in the L(beta) phase are only weakly bound. The unbinding transition appears to be driven by an abrupt increase in steric repulsion resulting from increased thermal undulations of the bilayers upon entering the fluid L(alpha) phase.     

From bunches of membranes to bundles of strings

Bunches of membranes and bundles of strings exhibit unbinding transitions from a bound state at low temperatures to an unbound state at high temperatures.N freely suspended manifolds unbind continuously at the unique unbinding temperatureT _u ^f which is independent ofN. The amplitudes of the critical singularities have a strongN-dependence, however, which implies that the critical region for the continuous transition becomes very small and the transition becomes very abrupt in the limit of largeN. IfN membranes or strings are bound to a rigid surface, they undergo a sequence of either two or ofN successive transitions. In general, the rigid surface affects the contact probabilities of the fluctuating manifolds. For effectively repulsive interactions, the contact exponent ₂ which governs the probability for local pair contacts satisfies the scaling relation ₂=d + whered and denote the dimensionality and the roughness exponent of these manifolds.Dedicated to Herbert Wagner on the occasion of his 60th birthday     

Pair superfluidity of three-body constrained bosons in two dimensions

We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first order to a continuous transition of the dilute Bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.     

Boundary between long-range and short-range critical behavior in systems with algebraic interactions

We investigate phase transitions of two-dimensional Ising models with power-law interactions, using an efficient Monte Carlo algorithm. For slow decay, the transition is of the mean-field type; for fast decay, it belongs to the short-range Ising universality class. We focus on the intermediate range, where the critical exponents depend continuously on the power law. We find that the boundary with short-range critical behavior occurs for interactions depending on distance r as r(-15/4). This answers a long-standing controversy between mutually conflicting renormalization-group analyses.     

The absence of phase transition for the classical XY-model on Sierpiński pyramid with fractal dimension D=2

For the spin models with continuous symmetry on regular lattices and finite range of interactions, the lower critical dimension is d?=?2. In two dimensions the classical XY-model displays Berezinskii–Kosterlitz–Thouless (BKT) transition associated with unbinding of topological defects (vortices and antivortices). We perform a Monte Carlo study of the classical XY-model on Sierpiński pyramids (SPs) whose fractal dimension is D = log?4/log?2?=?2 and the average coordination number per site is ≈ 7. The specific heat does not depend on the system size which indicates the absence of a long-range order. From the dependence of the helicity modulus on the cluster size and on boundary conditions, we draw a conclusion that in the thermodynamic limit there is no BKT transition at any finite temperature. This conclusion is also supported by our results for linear magnetic susceptibility. The lack of finite temperature phase transition is presumably caused by the finite order of ramification of SP.     

Griffiths singularities in unbinding of strongly disordered polymers

Griffiths singularities occurring in the unbinding of strongly disordered heteropolymers are studied. A model with two randomly distributed binding energies, -1 and -v, is introduced and studied analytically by analyzing the Lee-Yang zeros of the partition sum. It is demonstrated that in the limit v--> infinity the model exhibits a Griffiths type singularity at a temperature T(G)=O(1) corresponding to melting of long homogeneous domains of the low binding energy. For finite v>1 the model is expected to exhibit an additional, unbinding, transition at a high temperature T(M)=O(v).     

Statistical field theory for simple fluids: mean field and Gaussian approximations

We present an exact field theoretical representation of the statistical mechanics of simple classical liquids with short-range pairwise additive interactions. The action of the field theory is obtained by performing a Hubbard-Stratonovich transformation of the configurational Boltzmann factor. The mean field and Gaussian approximations of the theory are derived and applications to the liquid-vapour transition considered.     

Transport by Molecular Motors in the Presence of Static Defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors’ transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.     

Lattice energy and phase transition of alkaline earth chalcogenide

In this study, we have investigated the high-pressure structural phase transition of alkaline earth's chalcogenides within the framework of three-body potentials. We are considering short-range repulsive interactions up to the second nearest neighbors. The structural phase transition from the low-pressure NaCl (B1) to the high-pressure CsCl (B2) structure is estimated by Gibbs free energy calculations. The results are satisfactory and in agreement with the available experimental and other theoretical results.     

Size dependent thermal hysteresis in spin crossover nanoparticles reflected within a Monte Carlo based Ising-like model

Spin crossover compounds are photo-magnetic bistable molecular magnets with two states in thermodynamic competition: the diamagnetic low-spin state and paramagnetic high-spin state. The thermal transition between the two states is often accompanied by a wide hysteresis, premise for possible application of these materials as recording media. In this paper we study the influence of the system's size on the thermal hysteresis loops using Monte Carlo simulations based on an Arrhenius dynamics applied for an Ising like model with long- and short-range interactions. We show that using appropriate boundary conditions it is possible to reproduce both the drop of hysteresis width with decreasing particle size, the hysteresis shift towards lower temperatures and the incomplete transition, as in the available experimental data. The case of larger systems composed by several sublattices is equally treated reproducing the shrinkage of the hysteresis loop's width experimentally observed.     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

Charge fluctuation model of lattice vibrations

A new phenomenological model is proposed for the lattice dynamics of transition metals. It is based on the microscopic model of Sinha and Harmon and includes the effect of charge fluctuations coupled to atomic motions. The model has been found to reproduce very accurately the phonon dispersion curves for Nb with short-range charge fluctuations and interatomic interactions.     

The gravitational interaction of conical strings

Up to now calculations of the interaction of cosmic strings have neglected gravity. We consider the purely gravitational interactions that occur at large distances, using the conical line singularity for the gravitational field of a string. We construct spaces with multiple intersecting conical strings, that are exactly consistent with General Relativity, and which can be covered in a single Minkowski coordinate patch, using a Regge calculus type construction. We show that after two such strings pass through each other they remain connected by another string, and we derive the branching rules which govern the junction of three strings. These rules apply to conical type strings in any smoothly curved background, whether they are straight or curved, moving or stationary, and they show that, at the junction, the three strings must be as coplanar as is possible in such a space. For these results to be matched onto the short range results of Field Theory calculations, it is suggested that gravitational radiation must be introduced. This would mean that gravitation is not negligible in these interactions.     

Statistical mechanics of bilayer membranes in troubled aqueous media

We consider a bilayer membrane surrounded by small impurities, assumed to be attractive or repulsive. The purpose is a quantitative study of the effects of these impurities on the statistical properties of the supported membrane. Using the replica trick combined with a variational method, we compute the membrane mean-roughness and the height correlation function for almost-flat membranes, as functions of the primitive elastic constants of the membrane and some parameter that is proportional to the volume fraction of impurities and their interaction strength. As results, the attractive impurities increase the shape fluctuations due to the membrane undulations, while repulsive ones suppress these fluctuations. Second, we compute the equilibrium diameter of (spherical) vesicles surrounded by small random particles starting from the curvature equation. Third, the study is extended to a lamellar phase composed of two parallel fluid membranes, which are separated by a finite distance. This lamellar phase undergoes an unbinding transition. We demonstrate that the attractive impurities increase the unbinding critical temperature, while repulsive ones decrease this temperature. Finally, we say that the presence of small impurities in an aqueous medium may be a mechanism to suppress or to produce an unbinding transition, even the temperature and polarizability of the aqueous medium are fixed, in lamellar phases formed by parallel lipid bilayers.