Seminarium Fizyki Materii Skondensowanej

We present an exact solution and phase diagram of the anisotropic XY quantum chain in transverse magnetic field. On the phase diagram, there are lines of phase transitions in Ising universality class as well as the line of phasetransition of infinite order. We then pose two questions, which answer is not known for us:1) problem of universality of phase transitions in XY chain, in particularthose of infinite order, and2) the classification of phase transitions of infinite order.