The two dimensional XY spin glass in is studied numerically by a finite size defect energy scaling method at T = 0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T . Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent νs = νc ≈ 2.70. Preliminary results in 3d are also obtained.PACS numbers: 75.10. Nr, 05.70.Jk, 64.60.Cn The XY spin glass has been the subject of considerable attention and controversy for some time and is still not understood. It has been known since the seminal work of Villain [1] that vector spin glass models have chiral or reflection symmetry in addition to the continuous rotational symmetry. Consequently, the XY spin glass may have two different glass orders, a spin glass order and a chiral glass order. It is widely accepted and has become part of the spin glass folklore that, in two and three dimensions, chiral and spin variables decouple at long distances and order independently [2][3][4][5] although there is a hint that this may not hold in four dimensions [6]. Numerical estimates of the correlation length exponents ν in two dimensions, where both spin and chiral order set in at T = 0 as ξ s,c ∼ T −νs,c , indicate that ν c = 2.57 ± 0.003 and ν s = 1.29 ± 0.02 [5] which agree with older, less accurate estimates [2,3,7]. The decoupling of chiral and spin degrees of freedom seems to be well established by these numerical results, but some analytic work on special models [8][9][10] implies that, at least for XY spin glasses below their lower critical dimension d l > 2 when order sets in at T = 0, both correlation lengths diverge with the same exponent ν s = ν c . To add to the confusion, there is rather convincing evidence that chiral order sets in for 0 < T < T c , while spin glass order occurs only at T = 0 in 3d [2][3][4][11][12][13]. These numerical investigations have led to another piece of accepted folklore, namely that the lower critical dimension d l ≥ 4 for spin glass order [13,14]. A very recent simulation [5] concluded that earlier simulations are misleading because the spin defect energy began to grow with system size L at values of L just beyond the limit accessible to earlier attempts and that d l is slightly less than three. However, chiral order is robust in 3d. In 2d, all simulations agree that chiral and spin glass order set in at T = 0 but with different exponents ν c ≈ 2ν s ≈ 2.6.The theoretical situation is unclear since, to our knowledge, there is no unambiguous proof of any of the accepted folklore outlined above [16][17][18], numerical simulations are contradictory [5] and the analytic work on special models [8][9][10] is difficult to reconcile with the apparently unambiguous numerical simulations on the 2d XY spin glass. In this letter, we attempt to clarify the contradictory conclusions from numerical and analytic studies outlined above and to identify whic...

The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents θs ≈ −0.36 in 2D and θs ≈ +0.31 in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the ±J XY spin glass in 3D, we obtain a spin stiffness exponent θs ≈ +0.10 which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain θs < 0. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.

We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit, however, the spectrum becomes isotropic and compares well with the predictions of a simple capillary wave theory.

The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state configuration for a given realization of disorder. A numerical technique, which is exact in principle, is used to evaluate this energy and to estimate the stiffness exponent $\theta$. This method gives $\theta = -0.36\pm0.013$ in 2d and $\theta = +0.31\pm 0.015$ in 3d, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let