title: Completely packed O(n) loop models and their relation with exactly solved coloring models.
abstract: We investigate the completely packed O(n) loop model on the square lattice, and its generalization to an Eulerian graph model, which follows by including cubic vertices which connect the four incoming loop segments. This model includes crossing bonds as well. Our study was inspired by existing exact solutions of the so-called coloring model due to Schultz and Perk [Phys. Rev. Lett. 46, 629 (1981)], which is shown to be equivalent with our generalized loop model. We explore the physical properties and the phase diagram of this model by means of transfer-matrix calculations and finite-size scaling. The exact results, which include seven one-dimensional branches in the parameter space of our generalized loop model, are compared to our numerical results. The results for the phase behavior also extend to parts of the parameter space beyond the exactly solved subspaces. One of the exactly solved branches describes the case of nonintersecting loops and was already known to correspond with the ordering transition of the Potts model. Another exactly solved branch, describing a model with nonintersecting loops and cubic vertices, corresponds with a first-order, Ising-like phase transition for n>2. For 1<n<2, this branch is interpreted in terms of a low-temperature O(n) phase with corner-cubic anisotropy. For n>2 this branch is the locus of a first-order phase boundary between a phase with a hard-square, lattice-gas-like ordering and a phase dominated by cubic vertices. A mean-field argument explains the first-order nature of this transition.
authors: Lorentz Institute, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
authors: Yougang
authors: Y
authors: Wang
authors: Physics Department, Beijing Normal University, Beijing 100875, People's Republic of China.|State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
authors: Wenan
authors: W
authors: Guo
authors: Lorentz Institute, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
authors: Henk W J
authors: HW
authors: Blöte