Geometrical Properties of Loops and Cluster Boundaries
نویسنده
چکیده
We discuss how the statistical properties of the area and radius of gyration of single self-avoiding loops, and of Ising and percolation cluster boundaries, may be calculated using ideas of two-dimensional field theory. For cluster boundaries, we show that almost all loops have area C lnL+O(1), where L is the size of the system, and C is a calculable constant. We also compute the universal ratios 〈A〉l/〈R〉l of the area to the squared radius of gyration of loops of a given large perimeter l.
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