相关论文: On the Red-Green-Blue Model

In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes with distortion at most~$6$. It follows that lamplighter…

The two-replica Chayes-Machta-Redner (CMR) representation is one of the main proposed geometric signatures of spin-glass order in the short-range Edwards-Anderson model. Mean-field arguments and recent numerics suggest that the…

Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…

A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing…

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…

We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…

In the usual statistical model of a dense polymer (a single space-filling loop on a lattice) in two dimensions the loop does not cross itself. We modify this by including intersections in which {\em three} lines can cross at the same point,…

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an…

In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is…

We have theoretically investigated two-band models of graded-gap superlattices within the envelope-function approximation. Assuming that the gap varies linearly with spatial coordinate, we are able to find exact solutions of the…

It is shown, using asymptotically exact methods, that the two dimensional repulsive Hubbard model with strongly modulated interactions exhibits ``high temperature superconductivity". Specifically, the explicit modulation, which has the same…

We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…

This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…

Pair density modulation is a superconducting state, recently observed in exfoliated iron-based superconductor flakes, in which the superconducting gap oscillates strongly with the same periodicity as the underlying crystalline lattice. We…

In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…

Targeted color-dots with varying shapes and sizes in images are first exhaustively identified, and then their multiscale 2D geometric patterns are extracted for testing spatial uniformness in a progressive fashion. Based on color theory in…

Effects of the inter-layer couplings for the orthogonal dimer system SrCu$_2$(BO$_3$)$_2$ are discussed. The spin-gap $\Delta$ of the three-dimensional model is independent of the inter-layer couplings when they are small. Therefore at low…

The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains…

Using the (dynamical) density-matrix renormalization group method, we study the low-energy physics of three-leg antiferromagnetic Heisenberg model where the periodic boundary conditions are applied in the rung direction. We confirm that the…