Questions tagged [percolation]

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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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Estimation of Fisher exponent for a 2d percolation in our model comes around 1.9, instead of approx. 2.05. How to solve this error?

I am a biologist working on 2d percolation to model cellular phenomena. I am trying to find the value of fisher exponent 'tau' at the critical point. The sacling relation is that the number of ...
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1answer
18 views

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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119 views

Percolation in Bethe Lattice with Alternating Neighboor Numbers

Suppose we have a Bethe Lattice with alternating numbers of neighbours,starting from 3 and then 4 and so on. So the zeroth point has 3 neighbours, each of those 3 first neighbours has 4 neighbours (3 ...
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136 views

Speed of sound at phase transition — does percolation theory describe it?

Tl;dr: How does the speed of sound vary across a phrase transition? Although a phase transition might be "instantaneous" in terms of temperature, if we instead control Pressure and Volume then we ...
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1answer
245 views

Percolation theory: Is there a clear relationship between “probability of connection” and “effective porosity”?

Disclaimer: I am a geophysicist, not a physicist. Sometimes we speak a slightly different language and use different terms. Suppose you have an $N$ x $N$, 2-D rectangular lattice with bonds which ...
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2answers
85 views

Percolation theory: What is the critical amplitude for the “backbone” of a 2-D network?

Disclaimer: I am just learning about percolation theory for the first time, so I am not too familiar with some of the terminology. Suppose you have a 2-D square lattice with bonds connecting sites. ...
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1answer
124 views

Physical interpretation of power law cluster size distribution in percolation problem

In the site percolation problem, when the occupation probability $p \rightarrow p_c$, where $p_c$ is the critical probability. The characteristic length diverges, and assuming the usual scaling ansatz ...
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2answers
387 views

Is there a link between Percolation Theory and phase transitions?

Is there a direct link between phase transitions in physics and Percolation Theory (and the critical points in both cases) in the sense that the mechanism in one of them could be a special or ...
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42 views

What's that theorem? All RG operators flow to directed percolation?

I can't for the life of me get this theorem straight. I can remember neither the name nor it's statement and would be grateful for anyone who wants to toss out some wisdom. It pertains to the ...
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153 views

Percolation in Ultimate Frisbee (and Rugby, American Football, Basketball etc)

Question Has anyone ever investigated weather game dynamics in certain sports ever experiences a percolation-type transition with catching probability as the driver? Details I recently started ...
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0answers
32 views

Dynamic site percolation of independant random walkers on 2d square lattice

Really appreciate your help, I am stuck in a part of my research which I am not expert in. I have a 2-dimensional square lattice with periodic boundary conditions(torus). I am placing one walker at ...
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0answers
65 views

When does a finite size random graph percolate?

Assume we are simulating percolation on a 2d lattice. While the system is of finite size, we say that the critical state appears when a cluster connects two opposing ends of the lattice. The bigger ...
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1answer
131 views

Time for Two Reservoirs that are Connected with a Porous Medium to Equilibrate

I'm trying to calculate the time for the liquid in two connected reservoirs (open to the air) to equilibrate. The tricky part is the connecting region, which consists of a porous medium. I understand ...
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2answers
81 views

Is there a formulation for (self-)accelerating fluid flow through permeable medium?

I have a permeable system where is an accelerating fluid flow. Imagine a sponge that is squeezed. The fluid starts at rest, accelerates and flows out from the sponge. How to calculate the fluid speed? ...
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2answers
302 views

Phase transition without the Peierls' counter argument

Is there any proof of the existence of phase transition in models of statistical mechanics of the Ising type models without using the Peierls' argument and its variations? By models of the Ising type ...
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1answer
318 views

Percolation and number of phases in the 2D Ising model

Update. As my previous figure had conceptual mistakes I decided to change the picture to another, more instructive. After a long time I came back to try to understand an article on the Ising model. ...
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3answers
1k views

Why does correlation length diverge at the percolation threshold?

I'm reading a paper about electronic percolation. $p$ is the fraction of occupied bonds (or sites, depending on the model you're using, but I'll just use bonds), $p_c$ is the critical fraction of ...
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1answer
881 views

Numerical Ising Model: Swendsen–Wang algorithm, Percolation theory?

When you look at the original paper of Swendsen and Wang in 1987: "Nonuniversal critical dynamics in Monte Carlo simulations" it is somewhat mentioned that the proposed algorithm uses percolation ...
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56 views

Why do these papers show the wrong concavity to the conductivity near the percolation threshold?

I'm looking at two papers in particular: A. L. Efros and B. I. Shklovskii, Critical Behaviour of Conductivity and Dielectric Constant near the Metal-Non-Metal Transition Threshold, Phys. Status Solidi ...
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140 views

Physical, intuitive reason for divergence of dielectric constant at electronic percolation transition?

Several papers such as this (warning, PDF) and this (PDF again) talk about how, near the electronic percolation transition for a metallic 2D film, the real part of the dielectric constant diverges (...
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113 views

Random orientation percolation (Grimmett model) from the viewpoint of statistical mechanics

This is a rather soft question, but I would like to know how physicists would approach a problem which seems to be hard from the mathematical prospective. The Grimmett percolation model is defined ...
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1answer
410 views

The strong Markov property of Gibbs measures in 2D Ising Model

My background is that of a mathematician. I have a question about the two Dimensional Ising Model. I think the terminology I use is similar to the physical. I'm trying to understand the following ...
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2answers
112 views

Sampling typical clusters between distant points in subcritical percolation

I have on several occasions wondered how one might proceed in order to sample large subcritical Bernoulli bond-percolation clusters, say on the square lattice. More precisely, let's consider the ...
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1answer
1k views

Percolation in a 2D Ising model

For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence ...
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1answer
149 views

Have characteristics of a 'doubly percolated' lattice been described

Has a system where conducting sites can percolate by hopping over/tunnelling through a non-conducting site been described? If so what are the characteristics, and where can I find more details (such ...
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69 views

finding resistance from percolation theory with only energy disorder

Within an Miller-Abrahams random resistor model, finding the critical resistance when there is spatial disorder is simple as there is the bonding criterion $\int_0^{r_c} 4 \pi N r^2 dr = B_c \approx ...
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1answer
248 views

Definition regarding percolation

in a homework sheet studying bond-percolation on the Bethe lattice, a function $g(r)$ is introduced as "the probability of finding two nodes separated by a distance $r$ on the same cluster". Now ...