Related papers: Mean field approach to first and second order phas…
We study numerically the phase structure of the Ginzburg-Landau model, with particular emphasis on mass measurements. There is no local gauge invariant order parameter, but we find that there is a phase transition characterized by a…
For the structure of the thin electrical double layer~(EDL) and the property related to the EDL capacitance, we analyze boundary layer solutions (corresponding to the electrostatic potential) of a non-local elliptic equation which is a…
Theory of classical critical phenomena of Mott transition is developed for the dimensionality $d \le \infty$. Reconsidering a cluster dynamical mean-field theory (DMFT), Ginzburg-Landau free energy is derived in terms of hybridization…
We consider $\mathrm{SU}(N)$-symmetric Ginzburg-Landau models coupled to non-compact Abelian gauge field focusing on the case $N > 2$ at finite temperature. We show that, at least for sufficiently large gauge-field coupling constants, these…
We study a Ginzburg-Landau model of structural phase transition in two dimensions, in which a single order parameter is coupled to the tetragonal and dilational strains. Such elastic coupling terms in the free energy much affect the phase…
We formulate a general mean-field theory of a flat electric double layer in ionic liquids and electrolyte solutions with ions possessing static polarizability and a permanent dipole moment on a charged electrode. We establish a new…
We develop of a field-theoretic approach for the treatment of both the non-local and the non-linear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and…
Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are…
Recent advances in experimental and computational techniques have allowed for an accurate description of the adsorption of ionic liquids on metallic electrodes. It is now well established that they adopt a multi-layered structure, and that…
Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the…
The d-dimensional complex Ginzburg-Landau (GL) model is solved according to a variational method by separating phase and amplitude. The GL transition becomes first order for high superfluid density because of effects of phase fluctuations.…
The leaky dielectric model is widely used in simulating two-phase electrohydrodynamic (EHD) flows. One critical issue with this classical model is the assumption of Ohmic conduction, which makes it inadequate for describing the newly…
Recent experimental results indicate that phosphorus, a single-component system, can have two liquid phases: a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different…
We investigate electric-field effects in dilute electrolytes with nonlinear polarization. As a first example of such systems, we add a dipolar component with a relatively large dipole moment $\mu_0$ to an aqueous electrolyte. As a second…
The raise of the symmetry breaking mechanism by Landau[1] is a landmark in the studies of phase transitions. The Kosterlitz-Thouless phase transition[2-3] and the fractional quantum Hall effect[4], however, are believed to be induced by…
Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly-interacting environment, leading to the formation of discrete layers of charges at interfaces. Here, we propose a continuum theory that captures the…
Ionic liquids offer unique bulk and interfacial characteristics as battery electrolytes. Our continuum approach naturally describes the electrolyte on a macroscale. An integral formulation for the molecular repulsion,which can be…
We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a…
Localized traveling wave trains or pulses have been observed in various experiments in binary mixture convection. For strongly negative separation ratio, these pulse structures can be described as two interacting fronts of opposite…
We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of $N$ rod-like particles as $N\to\infty$, which yields an effective…