Questions tagged [percolation]
The percolation tag has no usage guidance.
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Connectivity of random geometric graph with open boundary conditions
I have a question regarding the existence of a closed-form solution of the connectivity in terms of the radius of vertices (disks) in a two-dimensional ($d=2$) random geometric graph (RGG) with open ...
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How to show random cluster models with non-integer $q$ have no local description?
It is known that the random cluster model with $q = 1$ corresponds to bond percolation, and $q = 2, 3, ... $ corresponds to the $q$-state Potts model. Both of these have a local description.
What ...
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Boundary/contour tracing of a binary image in Python
I'm studying percolation on a square lattice. I identify clusters on the binary lattice using the SciPy API ndimage.label. My goal is to study the external perimeter (hull) of each of these clusters. ...
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When $h>0$ and $0<T<\infty$, do up domains percolate in the Ising model?
I'm considering the Ising model in a field on a square lattice in $d$ dimensions:
$$H = -\sum_{\langle i j \rangle} \sigma_i \sigma_j - h \sum_{i} \sigma_i$$
As usual, $\langle i j\rangle$ refers to ...
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Correlation length for percolation theory [closed]
I am currently running a numerical simulation for site percolation. Using periodic boundary conditions I am attempting to determine the correlation length following the method set out in this paper ...
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Local statistical model for percolation
I am interested in classical statistical models with degrees of freedom with a finite configuration set on regular lattices, and Boltzmann weights depending on the configurations in a constant-size ...
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Is there any book on percolation theory that analyse bond percolation mathematically?
Introduction to percolation theory, by Stauffer and Aharony, deals with site percolation only. Is there any book which describes mathematically the cluster size distribution, mean cluster size etc for ...
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If a truncated power law distribution still has no characteristic length scale?
I do know that a power law distribution can extend from 0 to $+\infty$, so due to the shape of the distribution, there is no way to define an average value (this might be a characteristic length scale ...
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Question about 1D Percolation Theory [closed]
I am currently reading "Introduction to Percolation Theory" by Stauffer and Aharony and am doing the problems. Question 2.2 wants me to calculate a closed-form expression for the $k$-th ...
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Coffee quality and temperature
The question is about adjusting the size of particles of coffee powder to temperature.
It is said that properly grinding the coffee grains is cricual for making good coffee (I have an espresso ...
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2D Ising model and FK-percolation
Consider the 2D Ising model on the finite lattice $\Lambda$ with $+$ boundary conditions, i.e., all spins outside of $\Lambda$ are $=+1$. Let $\mathscr{E}_\Lambda^b$ denote the edges in $\Lambda$ and ...
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Percolation universality class
There's very good table of different universality classes:
Ising model lies in the same universality class with $\phi^4$ theory.
Ising in $d≥4$ have critical exponents for free scalar field.
But I ...
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A question on subcritical percolation
Consider some 2D lattice of infinite extent where each site can either be $0$ or $1$ with probability $p$. It is known there exists some critical probability $p_c$ below which clusters of $1$ values ...
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Is it possible to implement the Invaded Cluster Algorithm on a network of Ising spins rather than a lattice?
My main concern is how to know if a cluster has percolated the network. For a periodic square lattice it is easy to determine if the cluster percolates by looking at the size of the cluster (as given ...
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Percolation of electrical conductivity
When a metal is made of different conductivity parts, current passes the least resistive percolation path.
My question is “does this path depend on the amount of current?”
I think the path doesn’t ...
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