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We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some interesting features. For example, the spectrum is…
We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display non-standard critical behavior on the lattice under…
The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock…
The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin…
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
In the Constrained-degree percolation model on a graph $(\mathbb{V},\mathbb{E})$ there are a sequence, $(U_e)_{e\in\mathbb{E}}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open…
We study the transport properties of a one-dimensional spinful Fermi gas, after junction of two semi-infinite sub-systems held at different temperatures. The ensuing dynamics is studied by analysing the space-time profiles of local…
We investigate the scaling behaviour of a singular perturbation model within the geometrically linearized theory of elasticity involving data of higher lamination order. We study boundary data which are of staircase type and show rather…
The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact.…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains…
The $S=1/2$ antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd…
In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied.…
This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the…
The Peierls distortions in a two-dimensional electron-lattice system described by a Su-Schrieffer-Heeger type model extended to two-dimensions are numerically studied for a square lattice. The electronic band is just half-filled and the…
Models of Dynamical Electroweak Symmetry Breaking are expected to display a quasi-conformal scaling behaviour in order to accommodate experimental constraints. The scaling properties of a theory can be studied using finite volume…
We study the level structure of excitations at the "deconfined" critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J$-$Q$ model as an example. Energy gaps in…
We study a toy model for a superconductor on a bipartite lattice, where intrinsic pairing inhomogeneity is produced by two different coupling constants on the sublattices. The simplicity of the model allows for analytic solutions and tests…
Using two different methods, we have determined the rescaling of the scalar condensate $Z\equiv Z_\phi$ near the critical line of a 4D Ising model. Our lattice data, in agreement with previous numerical indications, support the behavior…
We numerically investigate a lattice regularized version of quantum electrodynamics in one spatial dimension (Schwinger model). We work at a density where lattice commensuration effects are important, and preclude analytic solution of the…