Two-dimensional-to-one-dimensional transition in narrow strips of percolating metal-insulator mixtures

The two-dimensional-to-one-dimensional transition in a thin strip of a percolating metal-insulator mixture is considered. It is shown that, for the nodes-and-links model of the infinite cluster, this transition occurs when the width of the strip is of the order of the two-dimensional correlation length ${\xi }_2$ times the logarithm of the strip's length expressed in units of ${\xi }_2$.