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    Bond percolation the square lattice

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    On an infinite square lattice one places bonds on the edges of the lattice with probability 1/2. What is the probability that two nearest neighbor vertices are connected?

    © BrainMass Inc. brainmass.com March 4, 2021, 6:02 pm ad1c9bdddf
    https://brainmass.com/physics/classical-mechanics/bond-percolation-square-lattice-25777

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    documentclass[a4paper]{article}
    usepackage{graphicx,amsmath,amssymb}
    newcommand{haak}[1]{left(#1right)}
    newcommand{rhaak}[1]{left [#1right]}
    newcommand{lhaak}[1]{left | #1right |}
    newcommand{ahaak}[1]{left{#1right}}
    newcommand{gem}[1]{leftlangle #1rightrangle}
    newcommand{gemc}[2]{leftlangleleftlangleleft. #1right | #2
    rightranglerightrangle}
    newcommand{geml}[1]{leftlangle #1right.}
    newcommand{gemr}[1]{left. #1rightrangle}
    newcommand{haakl}[1]{left(#1right.}
    newcommand{haakr}[1]{left.#1right)}
    newcommand{rhaakl}[1]{left[#1right.}
    newcommand{rhaakr}[1]{left.#1right]}
    newcommand{lhaakl}[1]{left ...

    Solution Summary

    It is explained how the problem can be solved using duality.

    $2.49

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