Related papers: Surface width of the Solid-On-Solid models
We study the low temperature $(2+1)$D Solid-On-Solid model on $[[1, L ]]^2$ with zero boundary conditions and nonnegative heights (a floor at height $0$). Caputo et al. (2016) established that this random surface typically admits either…
We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will…
A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown…
We examine the higher-spin gauge models which are free on-shell and whose cubic vertex is BRST-exact. We show that these are free off-shell as well as on-shell. The key equation for this relates the derivative of the total deformed action…
The superfluid-insulator transition in systems of lattice bosons is usually analyzed in the framework of the Bose-Hubbard model, and has been extensively studied by theory and simulations. Less attention has been paid to the remnants of the…
Relaxation of initially out-of-equilibrium rough interfaces in presence of thermal noise is investigated using Langevin formalism. During thermal equilibration towards the well-known roughening regime, three scaling regimes observed over…
Using the linearity property of the Mullins-Herring equation when the velocity is zero with a Gaussian noise, we obtain an analytic form for the global mean-square surface width and height-height correlation function. This can be used to…
We study the phase structure of QCD at finite temperature and density by numerical simulations on a lattice. The most important point for the numerical study at finite density is treatment of the sign problem. We propose a method to avoid…
Based on the Monte Carlo kinetic method, we investigated the formation mechanisms of periodical modulations arising along the length of one-dimensional structures. The evolution of initially cylindrical nanowires/slabs at temperatures lower…
A three-dimensional (3 D) multiple-relaxation-time (MRT) and a 3 D single-relaxation-time (SRT) lattice Boltzmann (LB) models are proposed for the solid-liquid phase change. The enthalpy conservation equation can be recovered from the…
We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…
We study scalar glueballs and scalar mesons at $T \neq 0$ in the soft wall holographic QCD model. We find that, using the Anti-de Sitter-Black Hole metric for all values of the temperature, the masses of the hadronic states decrease and the…
We study gradient models on the lattice $\mathbb{Z}^d$ with non-convex interactions. These Gibbs fields (lattice models with continuous spin) emerge in various branches of physics and mathematics. In quantum field theory they appear as…
We present the solution of a linear Restricted Solid--on--Solid (RSOS) model in a field. Aside from the origins of this model in the context of describing the phase boundary in a magnet, interest also comes from more recent work on the…
In this article, we propose a mathematical model which explains the formation of strong bonds during the relaxation process of a soft solid on a hard surface. As a result, the soft solid relaxes to a non zero residual stress level. The…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, $d_c=6$. This method is based on the observation that…
The power load to the divertor surfaces is a key concern for future devices such as ITER, due to the thermal limits on the material surface. One factor that characterizes the heat flux to the divertor is the fall off length in the…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $q$-state Potts model to order $z^{56}$ (i.e. $u^{28}$), $z^{47}$, $z^{43}$,…
The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional…