Critical Exponents of the Fully Frustrated 2-D Xy Model

Abstract

We present a detailed study of the critical properties of the 2-D XY model with maximal frustration in a square lattice. We use extensive Monte Carlo simulations to study the thermodynamics of the spin and chiral degrees of freedom, concentrating on their correlation functions. The gauge invariant spin-spin correlation functions are calculated close to the critical point for lattice sizes up to $240\times 240$; the chiral correlation functions are studied on lattices up to $96\times 96$. We find that the critical exponents of the spin phase transition are $ν=0.3069$, and $η=0.1915$, which are to be compared with the unfrustrated XY model exponents $ν=1/2$ and $η=0.25$. We also find that the critical exponents of the chiral transition are $ν_χ=0.875$, $2β=0.1936$, $2γ= 1.82$, and $2γ\>\prime=1.025$, which are different from the expected 2-D Ising critical exponents. The spin-phase transition occurs at $T_{U(1)}=0.446$ which is about 7\% above the estimated chiral critical temperature $T_{Z_{2}}= 0.4206$. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23\% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed. (TO APPEAR IN PRB)