Study of a generalized XY model using the correlation length*

The correlation length is examined in a generalized XY model where, together with the usual ferromagnetic interaction between spins, there is an additional nematic interaction that allows for half-vortices. The power of the correlation length is demonstrated in distinguishing different phases, thus fully reconstructing the phase diagram of the model. Moreover, it allows for further investigation of the tricritical region in the phase diagram where the paramagnetic, the nematic and the quasi-long-ranged phases meet. It shows that the Ising-type transition between the nematic and the quasi-long-range ordered phases stops at the tricritical point. Starting from this tricritical point, there is an intermediate range of different physics separates the two regions corresponding to the Ising-type and the Berzinskii-Kosterlitz-Thouless-type transitions.