Critical Properties of the TwoDimensional XY Model.
Abstract
The XY model, which describes the behavior of twocomponent spins interacting on a lattice, was studied. The phase transition into a low temperature phase with no long range order but with an infinite susceptibility was considered. Renormalization group transformations were constructed directly on the lattice and a cumulant expansion technique was used. On both the square and triangular lattices, a nontrivial phase transition was found in the twodimensional classical XY model. The inverse critical temperature (in dimensionless units or spinspin coupling constant) was 0.44 for the square lattice and 0.25 for the triangular lattice. The calculated critical exponents were approximately equal for the two cases, as expected from universality. The values of the critical exponents were 2.43 for the susceptibility, 1.38 for the correlation length, 0.76 for the specific heat, and 0.24 for the decay of the correlation function.
 Publication:

Ph.D. Thesis
 Pub Date:
 1976
 Bibcode:
 1976PhDT........24L
 Keywords:

 Physics: Condensed Matter;
 Crystal Lattices;
 Phase Transformations;
 Two Dimensional Models;
 Correlation;
 Critical Temperature;
 Specific Heat;
 Transformations (Mathematics);
 Atomic and Molecular Physics