Critical behavior of two-dimensional fully frustrated XY systems

Abstract

We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices L × L, L 10 3 . We show that the lowtemperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent ν eff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.

Bose-Einstein condensation and critical behavior of two-component bosonic gases

“…A similar situation arises in 2D frustrated twocomponent spin models, see, e.g., Ref. 73, and references therein. RG scaling arguments analogous to those used for the 3D case allow us to infer that the critical behavior of identical interacting hard-core bosonic components is again controlled by a decoupled BKT FP.…”

Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

“…respectively, where ε and ζ are the exponents associated with the expected leading corrections: [83,84]…”

Numerical investigation of the ageing of the fully frustratedXYmodel

“…[12]). The most recent Monte Carlo simulations [13,14,15,12] now show evidences in favor of the Ising universality class. The disagreement with older simulations may be due to the fact that the exponents tend to the expected Ising values only for large lattice sizes [15,12].…”

“…This collapse is not as good if logarithmic corrections are omitted. The asymptotic value of the FDR is estimated to be X ∞ = 0.385 (15). In contradistinction to the algebraic decay of the spin-spin correlation function, X ∞ does not present any evolution with the waiting time s. For comparison, we have performed a similar simulation for the pure XY model.…”