Editing Percolation analysis
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On such a system, it is possible to perform simulations considering different system sizes (with <math> L \times L </math> sites), using | On such a system, it is possible to perform simulations considering different system sizes (with <math> L \times L </math> sites), using | ||
periodic boundary conditions. In such simulations one can generate different system realizations for given values of <math> x </math>, and compute | periodic boundary conditions. In such simulations one can generate different system realizations for given values of <math> x </math>, and compute | ||
the fraction, <math> X_{\rm per}(x,L) </math>, of realizations with percolating clusters. For low values of <math> x, ( x \rightarrow 0 | the fraction, <math> X_{\rm per}(x,L) </math>, of realizations with percolating clusters. For low values of <math> x </math>, (<math> x \rightarrow 0 </math>) we will get <math> X_{\rm per}(x,L) \approx 0 </math>, whereas when <math> x \rightarrow 1 </math>, then <math> X_{\rm per}(x,L) \approx 1</math>. Considering the behavior of <math> X_{\rm per} </math> as a function of <math> x </math>, for different | ||
values of <math> L </math> the transition between <math> X_{\rm per} \approx 0 </math> and <math> X_{\rm per} \approx 1 </math> occurs more | values of <math> L </math> the transition between <math> X_{\rm per} \approx 0 </math> and <math> X_{\rm per} \approx 1 </math> occurs more | ||
abruptly as <math> L </math> increases. In addition, it is possible to compute the value of the occupancy probability <math> x_{c} </math> | abruptly as <math> L </math> increases. In addition, it is possible to compute the value of the occupancy probability <math> x_{c} </math> | ||
at which the transition would take place for an infinite system ( | at which the transition would take place for an infinite system (so to say, in the thermodynamic limit). | ||
=== Finite-size scaling === | === Finite-size scaling === |