Critical behavior of the q-state clock model in three dimensions

Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy

We study the three-dimensional XY model with a Zq anisotropic term. At temperatures T<Tc this dangerously irrelevant perturbation is relevant only above a length scale Lambda, which diverges as a power of the correlation length, Lambda approximately xi aq. Below Lambda the order parameter is U(1) symmetric. We derive the full scaling function controlling the emergence of U(1) symmetry and use Monte Carlo results to extract the exponent aq for q=4,...,8. We find that aq approximately a4(q/4)2, with a4 only marginally larger than 1. We discuss these results in the context of U(1) symmetry at deconfined quantum-critical points separating antiferromagnetic and valence-bond-solid states in quantum spin systems.

Finite-size-scaling analysis of the XY universality class between two and three dimensions: an application of Novotny's transfer-matrix method

Based on Novotny's transfer-matrix method, we simulated the (stacked) triangular Ising anti-ferromagnet embedded in the space with the dimensions variable in the range 2 < or = d < or = 3. Our aim is to investigate the criticality of the XY universality class for 2 < or = d < or = 3. For that purpose, we employed an extended version of the finite-size-scaling analysis developed by Novotny, who utilized this scheme to survey the Ising criticality (ferromagnet) for 1 < or = d < or = 3. Diagonalizing the transfer matrix for the system sizes N up to N = 17 , we calculated the d -dependent correlation-length critical exponent nu(d). Our simulation result nu(d) appears to interpolate smoothly the known two limiting cases, namely, the Kosterlitz-Thouless (KT) and d = 3 XY universality classes, and the intermediate behavior bears close resemblance to that of the analytical formula via the 1/N-expansion technique. Methodological details including the modifications specific to the present model are reported.