Related papers: Discrete approximations to vector spin models
A problem of practical significance is the analysis of large, spatially distributed data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show that the spatial correlations between variables can…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
A previously tested differential equation method for generating low temperature series expansion for diagonal spin-spin correlation functions in the d=2 Ising model is extended to generate the non-universal terms for arbitrary separation of…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the…
By means of parallel tempering Monte Carlo simulations we find strong evidence for a finite-temperature spin-glass transition in a system of diluted classical Heisenberg dipoles randomly placed on the sites of a simple cubic lattice. We…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
We address the following important question: how to distinguish Kitaev models experimentally realized on small lattices from other non-topological interacting spin models. Based on symmetry arguments and exact diagonalization, we show that…
We consider charge and spin transport in the one-dimensional Hubbard model at infinite temperature, half-filling and zero magnetization. Implementing matrix-product-operator simulations of the non-equilibrium steady states of…
Using transfer-matrix method a correspondence between $2D$ classical spin systems ($2D$ Ising model and six-vertex model) and $1D$ quantum spin systems is considered. We find the transfer matrix in two limits - in a well-known…
We derive thermodynamically consistent models for diblock copolymer solutions coupled with the electric and magnetic field, respectively. These models satisfy the second law of thermodynamics and therefore are therefore thermodynamically…
Anisotropy is important for the existence of true long range order in two dimensional (2D) systems. This is firmly exemplified by the $q$-state clock models in which discreteness drives the quasi-long range order into a true long range…
We present a theoretical framework for evaluating effective interactions between localized spins mediated by itinerant electrons in double-exchange models. Performing the expansion with respect to the spin-dependent part of the electron…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance $r$ as $1/r^\alpha$ in $D=2$ and $3$ spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime…
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous…
Using high temperature series we calculate temperature derivatives of the spin-spin and density-density correlation functions to investigate the low energy spin and charge excitations of the two-dimensional t-J model. We find that the…
We propose a continuum model of percolation in two dimensions for overlapping disks with spin. In this model the existence of bonds is determined by the distance between the centers of the disks, and by the scalar product of the (randomly)…
This work addresses models (e.g. potential models of directed orbital systems- the manganates) in which an effective reduction dimensionality occurs as a result of a new symmetry which is intermediate between that of global and local gauge…
We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled…