  We present detailed Monte Carlo results for a two-dimensional grain boundary
model on a lattice. The effective Hamiltonian of the system results from the
microscopic interaction of grains with orientations described by spins of unit
length, and leads to a nearest-neighbour interaction proportional to the
absolute value of the angle between the grains. Our analysis of the correlation
length xi and susceptibility chi in the high-temperature phase favour a
Kosterlitz-Thouless-like (KT) singularity over a second-order phase transition.
Unconstrained KT fits of chi and xi confirm the predicted value for the
critical exponent nu, while the values of eta deviate from the theoretical
prediction. Additionally we apply finite-size scaling theory and investigate
the question of multiplicative logarithmic corrections to a KT transition. As
for the critical exponents our results are similar to data obtained from the XY
model, so that both models probably lie in the same universality class.
