2D random-axes XY magnet

The 2D XY model with random anisotropy h(x) cosn phi (h(x)=0, n is the order of anisotropy) is discussed. For eta =1,2 the system displays no phase transition. For eta >or=3 there is a temperature range T*<T<T c where random fields are unimportant and the low-temperature phase of the 'pure' XY model is revealed. In the range of T<T* there is essential renormalisation of the parameters T and h, namely T to T*, h to 0, so that low temperatures are unachievable. In any case no spin glass is observed, while susceptibility with respect to h identical to h(x) not=0 exhibits a quasicusp similar to that of the spin glasses.