mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as...

In statistical mechanics, the two-dimensional square lattice Ising model is a simple lattice model of interacting magnetic spins, an example of the class...

coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance...

triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points. Patterns of seven overlapping circles appear in historical...

on percolation in random sequential adsorption of linear k-mers on square lattices". Phys. Rev. E. 91 (1): 012109. arXiv:1412.7267. Bibcode:2015PhRvE...

the possibility of different structural phases.The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase...

Lattice gas automata (LGCA), or lattice gas cellular automata, are a type of cellular automaton used to simulate fluid flows, pioneered by Hardy–Pomeau–de...

just a lattice, mesh, or grid. Moreover, these terms are also commonly used for a finite section of the infinite graph, as in "an 8 × 8 square grid"....

hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper...

occurs. The most common percolation model is to take a regular lattice, like a square lattice, and make it into a random network by randomly "occupying" sites...

the 3-by-3 square lattice, generalizations have been proposed in the form of the least amount of lines needed on an n-by-n square lattice. Or, in mathematical...

^{n}} ⁠ whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. ⁠ Z n {\displaystyle...

In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones...

infinite lattice graphs, pc cannot be calculated exactly, though in some cases pc there is an exact value. For example: for the square lattice ℤ2 in two...

Other lattices include a linear chain, which is a very simple lattice which we will shortly use for modeling phonons. (For other common lattices, see crystal...

intended structure is likely to succeed or fail. In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability...

Bethe lattice (also called a regular tree) is an infinite symmetric regular tree where all vertices have the same number of neighbors. The Bethe lattice was...

its period lattice) can be a square, and for three of these groups, p4, p4m, and p4g, it must be a square. The inscribed circle of a square is the largest...

crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base...

emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The idea has been generalized in several different...

given lattice? More unsolved problems in mathematics In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that...

is NP-complete. Different versions of lattice proteins may adopt different types of lattice (typically square and triangular ones), in two or three dimensions...

85.3542%, if only hexagonal lattice clusters are disallowed, and 85.2514% if one disallows also deformed square lattice clusters. An analytical and closed-form...

hexagonal lattice which is the translate of the translational lattice. Scaling of a lattice divides the number of points per unit area by the square of the...

Laboratory in the 1940s, studied the growth of crystals, using a simple lattice network as his model. At the same time, John von Neumann, Ulam's colleague...

integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers, which form a square lattice in the complex plane. The...

given city block distance of the center dot on a regular square lattice. While centered square numbers, like figurate numbers in general, have few if any...

of frustration was thoroughly studied. In their previous work on a square lattice of frustrated magnets, they observed both ice-like short-range correlations...

model. The model has since been studied on the infinite lattice, on other (non-square) lattices, and on arbitrary graphs (including directed multigraphs)...

a two-dimensional square lattice, with magnetic interactions occurring only between nearest neighbors. In this model, each lattice site is given a spin...