New Critical Point for Two Dimensional XY -Type Models

Douglas M. Lublin

Anna Jonsson, Petter Minnhagen, Mats Nylén

A new critical point is established through Monte Carlo simulations for a class of two dimensional XY models with a modified nearest-neighbor spin interaction. The critical exponents found are \ensuremath{\nu}\ensuremath{\approxeq}1.4, \ensuremath{\beta}\ensuremath{\approxeq}0.6, and an \ensuremath{\alpha}0, consistent with hyperscaling. The phase transition is interpreted as a vortex-unbinding transition. Comparisons are made with the phase diagram of the two dimensional Coulomb gas and with the spin-1/2 XY model.

David Paul Landau, R.W. Gerling

Gesualdo Delfino A, Noel Lamsen

Abstract We show that scale-invariant scattering theory allows to exactly determine the critical points of two-dimensional systems with coupled and Ising order parameters. The results are obtained for N continuous and include criticality of the loop gas type. In particular, for N = 1 we exhibit three critical lines intersecting at the Berezinskii–Kosterlitz–Thouless transition point of the Gaussian model and related to the Z 4 symmetry of the isotropic Ashkin–Teller model. For N = 2 we classify the critical points that can arise in the XY-Ising model and provide exact answers about the critical exponents of the fully frustrated XY model.

Lars Melwyn Jensen

Yong Baek Kim, Xiao-Gang Wen

We use a large-N renormalization-group (RG) method to study a model of interacting boson system with a quenched random potential. In the absence of impurities, the pure boson system has a critical point that describes the superfluid--Mott-insulator (SF--MI) transition. The SF--MI transition of d-dimensional bosons belongs to the (d+1)-dimensional XY model universality class. In this paper, we study the dirty-boson critical points in the neighborhood of this pure SF--MI critical point. In general, the on-site random potential in the original lattice model gives two types of randomness in the effective-field-theoretic action. One is the randomness in the effective on-site repulsion w(x) and the other is the randomness of the chemical potential u(x). It turns out that d=2 is the critical dimension for both types of disorder but the roles of these two types of disorder are reversed as d=2 is crossed. Applying \ensuremath{\epsilon}=d-2 expansion, we found coupled RG equations for both kinds of randomness which reveal several nontrivial critical points. All the weak random fixed points we found have three or more relevant directions. We conclude that the direct SF--MI transition is unlikely to occur near two dimensions.