Related papers: Loop Model with Generalized Fugacity in Three Dime…
Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only…
Evaluating accessible conformational space is computationally expensive and thermal motions are partly neglected in computer models of molecular interactions. This produces error into the estimates of binding strength. We introduce a method…
We study the folding of the regular triangular lattice in three dimensional embedding space, a model for the crumpling of polymerised membranes. We consider a discrete model, where folds are either planar or form the angles of a regular…
Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…
We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these…
Using the combinatorics of two interpenetrating face centered cubic lattices together with the part of calculus naturally encoded in combinatorial topology, we construct from first principles a lattice model of 3D incompressible…
The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model. It has been conjectured that both the spin and the…
We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter…
Two discrete N-level alternatives to the popular imaginary cubic oscillator are proposed and studied. In a certain domain ${\cal D}$ of parameters $a$ and $z$ of the model, the spectrum of energies is shown real (i.e., potentially,…
The fully-packed loop model of closed paths covering the honeycomb lattice is studied through its identification with the $sl_q(3)$ integrable lattice model. Some known results from the Bethe ansatz solution of this model are reviewed. The…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices.
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
We study the problem of "phantom" folding of the two-dimensional square lattice, in which the edges and diagonals of each face can be folded. The non-vanishing thermodynamic folding entropy per face $s \simeq .2299(1)$ is estimated both…
Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view…
We investigate, via Monte Carlo simulations, the phase structure of a system of closed, nonintersecting but otherwise non-interacting, loops in 3 Euclidean dimensions. The loops correspond to closed trajectories of massive particles and we…
We perform numerical scattering experiments on a Lorentz array of disks centered on a triangular lattice with L columns and study its transmission and reflection properties. In the finite horizon case, the motion of the particles may be…
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations (dubbed fractons), and a ground state…
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a…