Related papers: Loop transfer matrix and gonihedric loop diffusion
Context: Radiative transfer modelling of expanding stellar envelopes is an important task in their analysis. To account for inhomogeneities and deviations from spherical symmetry, it is necessary to develop a 3D approach to radiative…
We demonstrate the application of our 3D radiative transfer framework in the model atmosphere code PHOENIX/3D for a number of spectrum synthesis calculations for very different conditions. The 3DRT framework discussed in the previous papers…
The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model…
L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass…
In this article we discuss the modelling of elastic and electromagnetic wave propagation through one- and two-dimensional structured piezoelectric solids. Dispersion and the effect of piezoelectricity on the group velocity and positions of…
We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect…
We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer…
We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and…
We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…
We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number…
This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a…
In this Letter we show that an arbitrarily good approximation to the propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may be obtained with polynomial computational resources in n and the error \epsilon, and…
We consider coupled waveguide lattices as an architecture that implement a wide range of multiport transformations. In this architecture, a particular transfer matrix is obtained through setting the step-wise profiles of the propagation…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
We introduce in a natural and straigthforward way the $loop$ (Lagrangian) $representation$ for the partition function of pure compact lattice QED. The corresponding classical lattice loop action is proportional to the quadratic area of the…
Starting from the known representation of the partition function of the 2- and 3-D Ising models as an integral over Grassmann variables, we perform a hopping expansion of the corresponding Pfaffian. We show that this expansion is an exact,…
We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system…
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of…