STATISTICAL PROPERTIES OF STRINGS

We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global U(1) cosmic strings, or equ ivalently vortices in superfluid He-4. We use a new method which avoid s the specification of boundary conditions on the lattice. We therefor e do not have the artificial distinction between short and long string loops or a ''second phase'' in the string network statistics associat ed with strings winding around a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities associated with the cubic latti ces of previous work. We find that the percentage of infinite string i s somewhat lower than on cubic lattices, 63% instead of 80%. We also i nvestigate the Hagedorn transition, at which infinite strings percolat e, controlling the string density by rendering one of the equilibrium states more probable. We measure the percolation threshold, the critic al exponent associated with the divergence of a suitably defined susce ptibility of the string loops, and that associated with the divergence of the correlation length.