The issue of the number, nature and sequence of phase transitions in fully frustrated two-dimensional XY models (FFXY) is a highly non trivial one due to the complex interplay between the continuous and discrete degrees of freedom which characterize such systems. In this contribution we attach such a problem by means of analytical as well as numerical techniques. From an analytical point of view, we show how the U(1)? Z2 symmetry of the FFXY model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at ‘paired states’ fillings ?=1 [1]. The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the physical properties of the FFXY model. The whole phase diagram is recovered by perturbing the TM model (c = 2) with relevant operators and by analyzing the corresponding RG flow. An unbinding phenomenon of kink-antikink states takes place which in turn gives rise to a massless line flow from the Z2 degenerate vacuum of the TM to the infrared fixed point with c = 3/2. In this way the Z2 non-invariant degrees of freedom of the TM decouple and the partition function gets reduced to the c=3/2 one with the consequent loss of the ground state degeneracy [2]. From a numerical point of view [3,4] we perform Monte Carlo simulations of the staggered magnetization, the helicity modulus and the fourth-order helicity modulus on a generalized FFXY model, which has the same symmetries and the same degrees of freedom as the FFXY model: indeed the FFXY model is a particular case of the generalized one. Finally we compare the results obtained in order to clarify the underlying physical picture and to shed new light on the whole phase diagram of the FFXY model.

[1] G. Cristofano, G. Maiella, V. Marotta, Mod. Phys. Lett. A 15 (2000) 1679; G. Cristofano, G. Maiella, V. Marotta, G. Niccoli, Nucl. Phys. B 641 (2002) 547. [2] G. Cristofano, V. Marotta, P. Minnhagen, A. Naddeo, G. Niccoli, J. Stat. Mech.: Theor. Exp. 11 (2006) P11009. [3] P. Minnhagen, B. J. Kim, S. Bernhardsson, G. Cristofano, Phys. Rev. B 76 (2007) 224403. [4] P. Minnhagen, B. J. Kim, S. Bernhardsson, G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, work in preparation.