A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Interface interactions in modulated phases,and upsilon points

Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where =0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Dichroism of (CH3NH3)2CdCl4 in the farinfrared

The dielectric constant of (CH₃NH₃)₂ CdCl₄ has been measured as a function of temperature in the submillimeter range. Freshly grown samples with a wide domain structure at room temperature show a pronounced dichroism in this spectral range which is caused by the orientation of the molecules in the room temperature orthorhombic phase and their response to the electromagnetic wave.     

Discontinuous and continuous transitions of collective behaviors in living systems

Living systems are full of astonishing diversity and complexity of life. Despite differences in the length scales and cognitive abilities of these systems, collective motion of large groups of individuals can emerge. It is of great importance to seek for the fundamental principles of collective motion, such as phase transitions and their natures. Via an eigen microstate approach, we have found a discontinuous transition of density and a continuous transition of velocity in the Vicsek models of collective motion, which are identified by the finite-size scaling form of order-parameter. At strong noise, living systems behave like gas. With the decrease of noise, the interactions between the particles of a living system become stronger and make them come closer. The living system experiences then a discontinuous gas-liquid like transition of density. The even stronger interactions at smaller noise make the velocity directions of the particles become ordered and there is a continuous phase transition of collective motion in addition.     

A Monte Carlo study of ant traffic in a uni-directional trail

In this study, we aim to investigate ant traffic in the uni-directional ant trail. We consider two types of ants moving in the trail: one of which smells well and the other does not. The theoretical base of the study is similar to that of the Nagel–Schreckenberg (NaSch) model, but we do not use the exclusion rule, the asymmetrical exclusion rule is employed instead. Ants are placed on the trail as mixed. By keeping the number of ‘poor-smelling ants’ constant, the traffic in the trail is studied as a function of the number of “good-smelling” ants and the evaporation rate probability of pheromone f$f$. The fundamental physical quantities, i.e., mean speed V$V$ and flux F$F$, interestingly show non-monotonic density dependence for some values of f$f$ at some densities.     

Photoinduced Ordering Transition in Microdroplets of Liquid Crystals with Azo‐Dendrimer

Ordering transitions are observed in azo‐dendrimer‐dissolved nematic liquid crystal (NLC) droplets dispersed in a glycerol matrix. The dendrimer molecules are spontaneously attached at the interface between NLC and glycerol, so that the nematic directors orient perpendicular to the interface, in the radial configuration. Photoisomerization makes the directors be tangential to the interface, in a photoinduced ordering transition from radial to bipolar structure. Similar experiments are conducted both in cholesteric (Ch) and smectic‐A (SmA) LC droplets. Complicated photoinduced ordering transitions are also observed in Ch and SmA droplets, and the associated molecular orientation changes are discussed. Photoisomerizable azo‐dendrimer molecules provide a possible way to control orientation, even in microdroplet systems in which the interface cannot be treated by conventional surface agents.     

Small-Angle and Wide-Angle X-Ray Scattering Study of Slow Relaxation Following Phase Transitions of New Bolaamphiphiles Based on N-(12-Betainylamino-Dodecane)-octyl β-D-Glucofuranosiduronamide Chloride

In the present study, we investigated the polymorphism and its time-dependence of a new series of bolaamphiphile molecules based on N-(12-Betainylamino-dodecane)-octyl β-D-Glucofuranosiduronamide Chloride. To obtain six members of this series, the length of the main bridging chain and the lateral chain were varied in order to modify the hydrophilic–lipophilic balance. Another chemical modification was to introduce a diacetylenic unit in the middle of the bridging chain to study the influence of the π–π stacking on the supramolecular organization of these molecules. Dry bolaamphiphiles self-organize in supramolecular structures such as lamellar crystalline structure, L_c; lamellar gel structure, L_β′; lamellar fluid structure, L_α; and lamellar isotropic structure, L. Thermal hysteresis of these structures, following phase transitions, are investigated by small-angle and wide-angle X-ray scattering. Once the thermal cycle is accomplished, the system remains in the kinetically stabilized undercooled high-temperature phase at the temperature of 20°C. Subsequently, the time-dependence of the relaxation to the thermodynamically stable phase is followed, and very slow relaxation for a period on the order of hours or days is observed. The study of the polymorphism and the stability of various phases of this new series of bolaamphiphiles—which are issued from natural primary resources (sugar beet and wheat) and thus interesting for potential application in pharmaceutical, cosmetics, or food industry—was undertaken in this work.