Related papers: Double Aztec Diamonds and the Tacnode Process
We investigate a two-dimensional tiling model. Even though the degrees of freedom in this model are discrete, it has a hidden continuous global symmetry in the infinite lattice limit, whose corresponding Goldstone modes are the…
In the inclined layer convection system, thermal convection in a Rayleigh--B\'enard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varying inclination angle ($\gamma$) and Rayleigh number…
This article has two main goals. First, it provides a self-contained exposition of the tangent plane method for the dimer model - a technique for analyzing arctic curves and limit shapes introduced by R. Kenyon and I. Prause (2020). Second,…
We study a model of $n$ one-dimensional non-intersecting Brownian motions with two prescribed starting points at time $t=0$ and two prescribed ending points at time $t=1$ in a critical regime where the paths fill two tangent ellipses in the…
A set of tiles for covering a surface is composed of two types of tiles. The base shape of each one of them is a diamond or rhombus, both with angles 60 and 120 degrees. They are distinguished by labeling one as an acute diamond with a base…
A mechanical diamond, a classical mechanics of a spring-mass model arrayed on a diamond lattice, is discussed topologically. Its frequency dispersion possesses an intrinsic nodal structure in the three-dimensional Brillouin zone (BZ)…
We introduce a new symmetry class of domino tilings of the Aztec diamond, called the off-diagonal symmetry class, which is motivated by the off-diagonally symmetric alternating sign matrices introduced by Kuperberg in 2002. We use the…
Recently has been observed for some one-dimensional models that exhibit unexpected pseudo-transitions and quasi-phases. This pseudo-transition resembles a first- and second-order phase transition simultaneously. One of those models is the…
Topological defects are typically quantified relative to ordered backgrounds. The importance of these defects to the understanding of physical phenomena including diverse equilibrium melting transitions from low temperature ordered to…
Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional…
Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of…
The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the…
A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. DTCs promise profound applications in precision time-keeping and other…
Topology and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three significant research directions: competition between distinct interactions, as in the multiple intertwined phases,…
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter $\eps> 0$. The domain has two cusps, one pointing up and one pointing down. In the limit…
We study the gap probabilities of the single-time Tacnode process. Through steepest descent analysis of a suitable Riemann-Hilbert problem, we show that under appropriate scaling regimes the gap probability of the Tacnode process…
Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases. Such gapless topological states have been accomplished by a…
The Roche limit, or the threshold separation within which a celestial object (the donor) M cannot remain in a stable configuration due to a companion's tidal field, has been well established when M is in hydrostatic equilibrium and has…
We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a…
Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and…