Ground-state correlations and universality in two-dimensional fully frustrated systems

The spin-spin correlation function in the ground state of some two-dimensional fully frustrated spin models are investigated. The correlations are long ranged and decay as 1r^η, where r is the distance between the two spins and η=1/2. This result is true for both the square and triangular fully frustrated lattices, thus suggesting that these models form a universality class. It is shown that the fully frustrated Ising model on a square lattice can be mapped exactly into a special Baxter model. The spin-spin correlation function of this Baxter model can be calculated exactly. The ground state of the fully frustrated square Ising model corresponds to the free fermion point of the F model and therefore, through duality, to the decoupling point of the critical Baxter line. The relationship between the F model above the critical temperature and the Gaussian model above the multicritical point is discussed.