Related papers: The genus-zero five-vertex model
This paper aims to present a systematic study on the Gauss images of complete minimal surfaces of genus 0 of finite total curvature in Euclidean 3-space and Euclidean 4-space. We focus on the number of omitted values and the total weight of…
We study subleading corrections to the genus-zero free energy of the $\mathcal{N}=3$ Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar…
The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this…
We study limit shapes in two equivalent models: the six-vertex model in the $c\to0$ limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve…
Here I review vectorial type condensation due to a non zero chemical potential associated to some of the global conserved charges of the theory. The phase structure is very rich since three distinct phases exists depending on the value…
The free fermion condition of the six-vertex model provides a 5 parameter sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing…
A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…
Experimental determination of absolute surface energies remains a challenge. We propose a simple method based on two independent measurements on 3D and 2D equilibrium shapes completed by the analysis of the thermal fluctuation of an…
In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model…
Stimulated by the recent attention given to the texture zeros found in the quark mass matrices sector of the Standard Model, an analytical method for identifying (or to exclude) texture zeros models will be implemented here, starting from…
We introduce a planted vertex cover problem on regular random graphs and study it by the cavity method of statistical mechanics. Different from conventional Ising models, the equilibrium ferromagnetic phase transition of this binary-spin…
We analyze the equilibrium states of quantum lattice model with local multi-well potentials for Sn$_2$P$_2$S$_6$ ferroelectric crystals using the mean and Gaussian curvatures ($H$, $K$), curvedness ($C$) and shape index ($S$). From the…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
We study numerically the density profile in the six-vertex model with domain wall boundary conditions. Using a Monte Carlo algorithm originally proposed by Allison and Reshetikhin we numerically evaluate the inhomogeneous density profiles…
The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line…
We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional…
This is the second paper in a series of papers analyzing angled crested type water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume that the fluid is inviscid, incompressible, irrotational and…
We construct a UV completion of the relaxion in a warped extra dimension. We identify the relaxion with the zero mode of the fifth component of a bulk gauge field and show how hierarchically different decay constants for this field can be…
Surface energies and surface elasticity largely affect the mechanical response of nanostructures as well as the physical phenomenon associated with surfaces such as evaporation and adsorption. Studying surface energies at finite…
We examine a dark energy model where a scalar unparticle degree of freedom plays the role of quintessence. In particular, we study a model where the unparticle degree of freedom has a standard kinetic term and a simple mass potential, the…