Questions tagged [lattices]
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85
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Find more relationships with LatticeReduce
I'm using LatticeReduce to find linear relationships in these trigonometric expressions,
...
- 7,138
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1
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54
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Sum on a lattice where variables can only take two values (Ising lattice gauge theory)
I want to study the Ising Gauge Theory which has the Hamiltonian
\begin{equation}
\mathcal{H} = -J \sum_{n,\mu,\nu} \sigma_3(n,\mu)\sigma_3(n+\mu,\nu)\sigma_3(n+\mu+\nu, -\mu)\sigma_3(n+\nu, -\nu)
\...
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Intersection of region with triangular lattice in 2D
Is there a function that finds all points that lie in specified region and also are part of triangular lattice defined by {Sqrt[3] i, 3 (2 j + Mod[i, 2])} for ...
- 20.1k
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Calculate the 1st Brillouin zone with given lattice basis vectors
Given two basis vectors in the 2-dimensional momentum space b1, b2, I want to write a function that returns the 1st Brillouin zone:
...
- 179
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2
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Identifying lattice squares that are intersected by a closed curve
Given a lattice of unit squares I would like to find the number of squares that a curve (in the example below the curve is a circle) passes through and the number of squares that totally reside inside ...
- 777
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Image plot of integer lattice through a map
Is there a way to plot (in the real line) the points corresponding to the image of
$$
L(n_{1},n_{2})=\alpha\cdot n_{1}+\beta\cdot n_{2},
$$
where $\alpha$ and $\beta$ are real numbers to be chosen and ...
- 93
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0
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108
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What is LatticeReduce minimizing?
According to the manual page on LatticeReduce, The product of the norms of lattice vectors will decrease. The claim seems to be true for small lattices, but, I cannot confirm this for higher ...
- 1,460
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Filling the space with rectangles
Following up on my previous question, I now seek to fill a matrix $m \times n$ with rectangles. Henrik Schumaker had provided some code in his answer to the previous question:
...
- 1,029
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Efficient algorithm for Euclidean distance on a lattice [closed]
I am unable to code the problem in Mathematica. For the problem, please see the attached image. Help in this regard will be greatly appreciated.
The statement of the problem is as follows:
Consider a ...
- 71
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Plotting a function on a triangular lattice
I am new to Mathematica, and am unsure on how to start this.
I am working with a triangular lattice $\mathcal{T}$ with basis vectors $(1,0)$ and$\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)$, and have ...
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Plotting of probability density on a lattice and studying dynamics
I have a lattice described by a AdjacencyMatrix or Hamiltonian. This matrix has all the information of how each site is connected to another site with what hopping ...
- 633
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Arbitrary lattice graph in 2D
My purpose is to generate a graph representing a lattice, where the vertices are essentially the lattice sites. This lattice has to be periodic. That means the opposite boundaries are identical.
MWE ...
- 633
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1
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How to generate an heterogeneous mesh
I'd like to generate a mesh with a big variance in cell size. Something like
I'd prefer not to rely on a vertex model and perhaps use something simpler, like ...
- 4,903