THE CRITICAL-BEHAVIOR OF THE 3D X-Y MODEL AND ITS RELATION WITH FRACTAL PROPERTIES OF THE VORTEX EXCITATIONS

The relation between the fractal dimensionality of the vortex excitati ons and the critical exponents of the vortex phase transition in the 3 D X-Y model is studied. The helicity modulus of the model is expressed via the average ''vortex moment'' of the system, The average ''vortex moment'' is described in terms of the polymer theory. Using this appr oach we derive RG equations of the 3D X-Y model in the low fugacity li mit, considering the vortex loop as a polymer chain with critical expo nent nu(p). The critical exponents nu of the correlation length coinci de with nu(p).