Related papers: The genus-zero five-vertex model
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
The random vortex world-surface model is an infrared effective model of Yang-Mills dynamics based on center vortex degrees of freedom. These degrees of freedom carry topological charge through writhe and self-intersection of their…
Line-tension-induced {scenario of heterogeneous nucleation} is studied for a lens-shaped nucleus with a finite contact angle nucleated on a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension…
Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is…
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\rho$ and all pressures are finite…
We study the partition function and free energy of the Curie-Weiss model with complex temperature, and partially describe its phase transitions. As a consequence, we obtain information on the locations of zeros of the partition function.
We consider the interface problem between two incompressible and inviscid fluids in the presence of surface tension. Following the geometric approach of [Shatah,J.;Zeng,C. A priori estimates for Fluid Interface Problems. CPAM, vol.16, no.6,…
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to three special types of vertex-weighted oriented $m$-partite graphs. These formulas are functions of the weight and…
A surface model of Nambu and Goto is studied statistical mechanically by using the canonical Monte Carlo simulation technique on a spherical meshwork. The model is defined by the area energy term and a one-dimensional bending energy term in…
The complex-field zeros of the Random Energy Model are analytically determined. For T<T_c they are distributed in the whole complex plane with a density that decays very fast with the real component of H. For T>T_c a region is found which…
The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex…
An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The…
We consider a class of spin-type discrete systems and analyze their continuum limit as the lattice spacing goes to zero. Under standard coerciveness and growth assumptions together with an additional head-to-tail symmetry condition, we…
Particles that interact via a square-shoulder potential, consisting of an impenetrable hard core with an adjacent, repulsive, step-like corona, are able to self-organize in a surprisingly rich variety of rather unconventional ordered…
We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…
Classical descriptions of flapping propulsion near a free surface emphasize the energetic penalties of wave generation, treating the interface primarily as an energy sink. Here, we show that the same deformable boundary can also act as a…
We prove the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We also discuss the conditions under which this maximal map can be made into a complete…
Central configurations and relative equilibria are an important facet of the study of the $N$-body problem, but become very difficult to rigorously analyze for $N>3$. In this paper we focus on a particular but interesting class of…
We study various generalisations of rationally connected varieties, allowing the connecting curves to be of higher genus. The main focus will be on free curves $f:C\to X$ with large unobstructed deformation space as originally defined by…
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…