相关论文: The Arctic Circle Revisited

We consider the six-vertex model with the rational weights on an $s\times N$ square lattice, $s\leq N$, with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are…

We study the effects of thermal fluctuations on a small elastic ring. We derive analytical expressions for the correlation functions of the Euler angles, for the real space two--point correlation functions and for the probability…

Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and…

We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency…

Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite…

We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show…

We introduce a new computational methodology for the identification and characterization of free volume within/around atomistic configurations. This scheme employs a three-stage workflow, by which spheres are iteratively grown inside of…

We study the 19-vertex model of Statistical Mechanics in a square with the domain wall boundary condition. Using the minimal set of generating flip actions we build a parametrized dynamic version of the model. For all observed dynamic…

K\"ahler's geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U($N)\otimes$U($N)$…

Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of…

We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions, the latter case includes the presence of Grassmann valued non-diagonal boundary fields…

A class of kinetically constrained models with reflection symmetry is proposed as an extension of the Fredrickson-Andersen model. It is proved that the proposed model on the square lattice exhibits a freezing transition at a non-trivial…

We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free…

I review aspects of work done in collaboration with A. Zee and R. Scalettar \cite{fz1,fz2,fsz} on complex non-hermitean random matrices. I open by explaining why the bag of tools used regularly in analyzing hermitean random matrices cannot…

Scalars are widely used in cosmology to model novel phenomena such as the late-time cosmic acceleration. These are effective field theories with highly nonlinear interactions, including Horndeski theory/generalized galileon and beyond. We…

In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and…

We consider free-fermion chains where full and empty parts are connected by a transition region with narrow surfaces. This can be caused by a linear potential or by time evolution from a step-like initial state. Entanglement spectra,…

A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schroedinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane…

Finite systems in confining potentials are known to undergo structural transitions similar to phase transitions. However, these systems are inhomogeneous, and their "melting" point may depend on the position in the trap and vary with the…