Related papers: On a variational model for the continuous mechanic…
We introduce a family of two-dimensional lattice models of quasicrystals, using a range of square hard cores together with a soft interaction based on an aperiodic tiling set. Along a low temperature isotherm we find, by Monte Carlo…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
This work generalizes our previous works on fcc-bcc martensitic transformations to the larger family of transformations in the fcc-bcc-hcp system and to fcc-fcc mechanical twinning. The analytical expressions of the atomic displacements and…
We will present a consistent description of Hamiltonian dynamics on the ``symplectic extended phase space'' that is analogous to that of a time-\underline{in}dependent Hamiltonian system on the conventional symplectic phase space. The…
By perceiving gauge invariance as an analytical tool in order to get insight into the states of the "generalized Landau problem" (a charged quantum particle moving inside a magnetic, and possibly electric field), and motivated by an early…
We comment on zero- and low-temperature structural phase transitions, expecting that these comments might be relevant not only for this structural case. We first consider a textbook model whose classical version is the only model for which…
In this paper, we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model "diffusion-based" because its hamiltonian can be recovered from a simple dynamic procedure, which…
We apply a recently developed technique to determine adapted coordinates for the sixth degree Landau-deGennes potential, in which the potential is specially simple, to analyze the possibility of a direct transition between the fully…
We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo's definition. We survey…
We derive a microscopic theory for the structural dynamics in the vicinity of the glass transition for a liquid exposed to a one-dimensional periodic potential. The periodic potential breaks translational invariance, in particular, the…
We employ the projector quantum Monte Carlo simulations to study the ground-state properties of the square-lattice SU(4) Hubbard model with a $\pi$ flux per plaquette. In the weak coupling regime, its ground state is in the gapless Dirac…
Continuous phase transitions associated with the onset of a spontaneously broken symmetry are thought to be successfully described by the Landau-Ginzburg-Wilson-Fisher theory of fluctuating order parameters. In this work we show that such…
In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We solve the Ginzburg-Landau equation (GLE) for the mesoscopic thin film of the square shape in the magnetic field. In the limit of Ginzburg-Landau parameter $\kappa \to \infty$ we find a series of first and second order phase transitions…
We present an explicit example of a gauge symmetry breaking phase transition in heterotic models, the dynamics of which are not thermal and can be described in a well controlled manner throughout. The phase transition is driven by the…
Let $\{\xi_i\}_{i \geq 1}$ be a sequence of i.i.d.\ positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in $i$-th vertical column to another in the $(i+1)$-th vertical column by…