Magnetization: A characteristic of the Kosterlitz-Thouless-Berezinskii transition

In the low-temperature phase of the two-dimensional XY model, spin-spin correlations decay so slowly with distance that the thermodynamic limit is inaccessible. As a result the Mermin-Wagner theorem is inapplicable to any realizable system, and all have a measurable finite-size magnetization. We show that there is a regime of universal behavior near to the Kosterlitz-Thouless-Berezinskii transition. In experiments, the regime is identified by a magnetization exponent {β}=0.23, which we have calculated by a renormalization-group analysis. Monte Carlo simulations of an harmonic XY model clearly locate the boundaries of the universal regime, and identify it with vortex renormalization.