approach to critical phenomena (see below). A particular intuitive example is offered by the nonlinear O($N$) spin model defined on a lattice in the limit $N\to0$, where the high-temperature graphs form random self-avoiding walks.[@deGennes] In the early 1950ies, Feynman[@lambda] applied his approach to the superfluid phase transition in liquid $^4$He, and showed that, in this picture, Bose-Einstein condensation arises when the worldlines of individual particles combine to form large lines threading the entire system. In the late 1970ies,[@BMK; @Peskin; @TS; @StoneThomas; @Samuel] the approach was applied to phase transitions in relativistic lattice models possessing line-like topological defects, thus mapping these models onto the statistical mechanics problem of random loop configurations. The line defects were pictured as forming a grand canonical ensemble of fluctuation loops of arbitrary shape and length–a so-called *loop gas*. In the 1980ies, the statistical properties of such loop gases were further investigated in the context of cosmic strings and their role in phase transitions in the early universe, with the loop distribution given a central position,[@Copeland:1988bh; @Copetal] as well as in the context of deconfinement phase transitions, where percolation observables were introduced to characterize them.[@Patel:1983sc; @Hands:1989cg] More recently, these ideas were pursued further with the goal to 