Related papers: A Note on Wetting Transition for Gradient Fields
We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity. In particular, this result explains the counterintuitive phenomenon that…
In this paper, we derive closed form solutions for the quasi-stationary problems of moving heat sources within the gradient theory of heat transfer. This theory can be formally deduced from the two-temperature model and it can be treated as…
The non-equilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced…
Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation…
We investigate complete wetting and drying at sinusoidally corrugated solid walls, focusing on the effects of wall geometry and interaction range. Two distinct interaction models are considered: one incorporating only short-ranged (SR)…
We consider gradient models on the lattice $Z^d$. These models serve as effective models for interfaces and are also known as continuous Ising models. The height of the interface is modelled by a random field with an energy which is a…
Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is…
The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of $L \times M$ lattices where competing boundary fields $\pm H_1$ act on the first row or last row of the $L$ rows in the strip, respectively. We…
Complete wetting of geometrically structured substrates by one-component fluids with long-ranged interactions is studied. We consider periodic arrays of rectangular or parabolic grooves and lattices of cylindrical or parabolic pits. We show…
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant…
This paper develops a general approach to characterize the long-time trajectory behavior of nonconvex gradient descent in generalized single-index models in the large aspect ratio regime. In this regime, we show that for each iteration the…
We present, theoretical predictions and Monte Carlo simulations, for a simple three matrix model that exhibits an exotic phase transition. The nature of the transition is very different if approached from the high or low temperature side.…
Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…
We consider the Widom--Rowlinson model on $\mathbb{Z}^d$ subject to a symmetric i.i.d.\ random field. We prove that for dimensions $d\le 2$ any non-trivial random field leads to an absence of a phase transition. In contrast, in dimensions…
Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…
We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…
We study a charged scalar field in a bulk 3+1 dimensional anti-deSitter spacetime with a planar black hole background metric. Through the AdS/CFT correspondence this is equivalent to a strongly coupled field theory in 2+1 dimensions…
We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
Applying a variational method to a Gaussian wave ansatz, we have derived a set of semi-classical evolution equations for SU(2) lattice gauge fields, which take the classical form in the limit of a vanishing width of the Gaussian wave…