The scaling properties of different systems are found to be related in unexpected ways. The continuous unbinding of two membranes in three dimensions [4], for example, exhibits the same scaling properties as the unbinding of two domain boundaries or "strings" in two dimensions [11]. For 1-dimensional lines, there is even an intimate relationship between the scaling properties of bound and unbound states [12].
Both bundles of N strings in two dimensions [13] [14] and bunches of N membranes in three dimensions [15] undergo continuous unbinding transitions whereas bundles of N filaments unbind discontinuously in three dimensions [16]. In the continuous case, the N-dependence of the critical exponents remains an open issue [17].