Related papers: Universality class of the restricted solid-on-soli…
The Separating Hyperplane theorem is a fundamental result in Convex Geometry with myriad applications. Our first result, Random Separating Hyperplane Theorem (RSH), is a strengthening of this for polytopes. $\rsh$ asserts that if the…
We investigate a quantum phase transition between a Neel phase and a valence bond solid (VBS) phase, in each of which a different Z2 symmetry is broken, in a spin-1/2 two-leg XXZ ladder with a four-spin interaction. The model can be viewed…
We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits,…
The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different…
We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on…
The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using temperature-density, (T, rho),…
Given any smooth, suitably small initial data, which decays polynomially at infinity, we prove global regularity for the $3D$ relativistic massive Vlasov-Maxwell system. In particular, the compact support assumption, which is widely used in…
A numerical diagonalization technique with canonical Monte-Carlo simulation algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov-Kimball model on a…
By performing a high-statistics simulation of the $D=4$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high…
We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature $\kappa\ne 0$: the unit sphere $\mathbb S^2$, for $\kappa>0$, and the unit hyperbolic sphere $\mathbb H^2$, for…
We study the phase diagram of Q-state Potts models, for Q=4 cos^2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on…
We relate the notion of unitarity of a $SL(2,\mathbf{R})$ invariant field theory with that of a Schrodinger field theory using the fact that $SL(2,\mathbf{R})$ is a subgroup of Schrodinger group. Exploiting $SL(2,\mathbf{R})$ unitarity, we…
We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of…
We use Ginzburg-Landau theory to study the $H_{c2}$ transition in layered superconductors with field parallel to the layers, finding a continuous 3d freezing transition to a triangular vortex super-solid in the three-dimensional XY…
Modelling the propagation of a pulse in a dense {\em milieu} poses fundamental challenges at the theoretical and applied levels. To this aim, in this paper we generalize the telegraph equation to non-ideal conditions by extending the…
In relatively nice geometric settings, in particular, on Lipschitz domains, absolute continuity of elliptic measure with respect to the surface measure is equivalent to Carleson measure estimates, to square function estimates, and to…
In this paper, we propose a new covering technique localized for the trajectories of SGD. This localization provides an algorithm-specific complexity measured by the covering number, which can have dimension-independent cardinality in…
We study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between the heights at adjacent sites is no more than one. In addition…
We study the Oppenheimer--Snyder (OS) collapse problem in metric $f(R)$ gravity by matching a homogeneous dust Friedmann--Lema\^itre--Robertson--Walker (FLRW) interior to a generalized Vaidya exterior across a timelike hypersurface. In…
We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and…