@bachelorsthesis{2000H,
  title={A study of the phase transition in the planar spin model on square lattices using Monte Carlo simulations},
  author={Bradley L. Holland},
  month={June},
  year={2000},
  abstract={Using the Metropolis Monte Carlo technique, the two-dimensional planar spin model has been
simulated for square lattices of 256, 900, 3600, 4900, 8100 and 10000 spins.  The energy,
specific heat, angular square displacement, magnetization and susceptibility have been
calculated for all lattices at temperatures ranging from 0.1 k<SUB>B</SUB>/J to
2.0 k<SUB>B</SUB>/J (where J is the nearest-neighbour coupling). In addition, the helicity
modulus has been calculated for the 8100 spin lattice. It has also been confirmed that there
is a loss of long range order as the size of the system increases. Three expressions proposed
by Kosterlitz and Thouless relating lattice size and temperature with angular square
displacement, magnetization and internal energy were tested and confirmed. The specific
heat curve was plotted for all lattice sizes and a peak was found slightly above the
critical temperature at 1.03 k<SUB>B</SUB>/J. By using the Kosterlitz-Thouless theory
the critical temperature at which vortex pairs unbind was found by fitting the susceptibility
curve for the 10000 spin lattice. This critical temperature was also estimated from the drop
of the helicity modulus curve for the 8100-spin lattice. The critical temperature was found
to lie between 0.8 k<SUB>B</SUB>/J and 0.9 k<SUB>B</SUB>/J.},
  note={Supervised by S.K. Bose}
}