Related papers: An Exact Solution to a Three Dimensional Ising Mod…
The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state…
We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation which combines accuracy, computational efficiency and versatility. The solver, based on a mixed plane-wave / interpolating scaling function…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
A reformulation of the Thirring model as a gauge theory on both continuum spacetime and discretized lattice is reviewed. In (1+1) dimensions, our result reproduces consistently the bosonization of the massless Thirring model. In (2+1)…
For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct low-dimensional representations of the dynamical system, which allow the learning of nearly optimal…
Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…
We describe two distinct approaches for bosonization in higher dimensions; one is based on a direct comparison of current correlation functions while the other relies on a Master lagrangean formalism. These are used to bosonise the Massive…
This paper presents an extension of the unfolding operator technique, initially applied to two-dimensional domains, to the realm of three-dimensional thin domains. The advancement of this methodology is pivotal, as it enhances our…
We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus…
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093 (2008), arXiv:0811.3876] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045]. Several…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place…
We review a growing theoretical motivation and evidence that the number of dimensions actually reduces at high energies. This reduction can happen near the Planck scale, or much before, the dimensions that are reduced can be effective,…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
We provide a non-trivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy…
In this work, we extend the analysis of interacting bosons at 2D-1D dimensional crossover for finite size and temperature by using field-theory approach (bosonization) and quantum Monte Carlo simulations. Stemming from the fact that finite…
The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism…
I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system…