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.     

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 .     

Finite-size scaling study of a first-order temperature-driven symmetry-breaking structural phase transition

We present a study of finite-size effects in a model exhibiting a first-order temperature-driven symmetry-breaking structural phase transition in theL × cylindrical geometry in theL limit. Exact studies demonstrate the applicability of our scaling ansatz even in the one-dimensional limit, making this model ideal for studying finite-size effects. The scaling ansatz, similar to the previously developed ansatz for field-driven transitions, demonstrates that latent heat is crucial in driving these transitions. This ansatz is supported by a 2×2 phenomenological transfer matrix based upon the symmetries of the system; this produces an analytic free energy which has the scaling form. Order parameter probability distributions show that the high- and low-temperature phases coexist only in a small finite-size-affected regime near the bulk transition temperature; this regime vanishes exponentially fast asL diverges.     

Line intensities of acetylene: New measurements in the 1.5-μm spectral region and global modelling in the ΔP=10 series

Using the Fourier transform spectra of the acetylene molecule recorded near 1.5-μm, the intensities of 111 lines belonging to seven hot bands of the main isotopologue ¹²C₂H₂ have been retrieved by means of a multispectrum fitting procedure. Considering the density of lines in the spectra, and the fact that the measured bands are the weakest observed, the accuracy of the measurements is around 10%. At first stage, an empirical treatment of these data has been performed, leading to the vibrational transition dipole moment squared and some Herman–Wallis coefficients. Then the measured line intensities of this work and collected ones from the literature have been treated simultaneously within the framework of the effective operator approach.     

Systematic Tuning and Switching of Neutral and Ionic Phases in a Donor–Acceptor Chain Compound by Doping with Less‐Active Donors and by Pressure Application

The temperature‐induced stepwise neutral–ionic (N–I) phase transition in the covalently bonded donor–acceptor chain compound [Ru₂(2,3,5,6‐F₄PhCO₂)₄DMDCNQI] ? 2(p‐xylene) (2,3,5,6‐F₄PhCO₂^?=2,3,5,6‐tetrafluorobenzoate; DMDCNQI=2,5‐dimethyl‐N,N′‐dicyanoquinodiimine) was systematically tuned over a wide temperature range using two techniques: 1) A chemical technique based on doping with a less‐active donor unit [Ru₂^II,II(F₅PhCO₂)₄] (F₅PhCO₂^?=pentafluorobenzoate), thereby providing an isostructural doped series [{Ru₂^II,II(2,3,5,6‐F₄PhCO₂)₄}_1?x{Ru₂^II,II(F₅PhCO₂)₄}_xDMDCNQI] ? 2(p‐xylene), with x=0.06, 0.10, 0.21, and 0.24; and 2) a physical technique, which was the application of hydrostatic pressure to the doped compounds. The stepwise N–I transition observed in the original compound was systematically varied in terms of the viewpoints of both transition temperature and transition features (stepwise or monotonic) dependent on the amount of dopants x. Application of pressure efficiently tuned the N–I transitions, with the oxidation phases being dramatically modified by applying only weak pressure up to 4 kbar. Even in cases that led to N–I transitions in small domains of the chains at ambient pressure, the application of pressure caused an expansion of the domains that enabled N–I transitions, finally leading to a complete change in the oxidation state of the chains, from neutral to ionic, accompanied by a change from a paramagnetic state to a ferrimagnetically ordered state.     

Landau theory for isotropic,nematic, smectic-A,and smectic-C phases

ABSTRACT

We use the Landau theory of phase transitions to describe the phase diagram of a liquid crystal displaying the isotropic (i), nematic (N), smectic-A and smectic-C phases. The order parameter of the smectic-C phase is defined as the projection of the director on the plane of the smectic layers, vanishing in the smectic-A phase. We present a detailed phase diagram that shows transition between any two of these phases, containing a triple point INA, a Lifshitz point NAC, a tricritical at the NA line, and a critical end point IAC. As one approaches the NC line from the smectic-C phase, the tilt angle approaches a nonzero value, but if the AC line is approached, the tilt angle vanishes according to the distance to the AC line to the power 1/2.