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14
votes
2answers
54 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 ...
5
votes
1answer
417 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 ...
4
votes
1answer
211 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 ...
3
votes
1answer
123 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 ...
2
votes
1answer
91 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 ...
2
votes
1answer
51 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 ...
2
votes
1answer
153 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. ...
2
votes
0answers
48 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 ...
1
vote
0answers
21 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 ...
1
vote
0answers
26 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 ...
1
vote
0answers
53 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 ...