相关论文: Finite average lengths in critical loop models

Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only…

The fully-packed loop model of closed paths covering the honeycomb lattice is studied through its identification with the $sl_q(3)$ integrable lattice model. Some known results from the Bethe ansatz solution of this model are reviewed. The…

A critical dilute O($n$) model on the kagome lattice is investigated analytically and numerically. We employ a number of exact equivalences which, in a few steps, link the critical O($n$) spin model on the kagome lattice to the exactly…

A lattice model of critical dense polymers $O(0)$ is considered for the finite cylinder geometry. Due to the presence of non-contractible loops with a fixed fugacity $\xi$, the model is a generalization of the critical dense polymers solved…

We study a model of dilute oriented loops on the square lattice, where each loop is compatible with a fixed, alternating orientation of the lattice edges. This implies that loop strands are not allowed to go straight at vertices, and…

The phase diagram of the O(n) model, in particular the special case $n=0$, is studied by means of transfer-matrix calculations on the loop representation of the O(n) model. The model is defined on the square lattice; the loops are allowed…

The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3-12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related…

The Fully-Packed Loop (FPL) model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin in 1991. Using the two-component Coulomb-Gas approach of Kondev, de…

We derive the nested Bethe Ansatz solution of the fully packed O($n$) loop model on the honeycomb lattice. From this solution we derive the bulk free energy per site along with the central charge and geometric scaling dimensions describing…

We explore the phase diagram of an O(n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O(n) model, so that $n$ is not restricted to…

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use…

We study a class of loop models, parameterized by a continuously varying loop fugacity n, on the hydrogen-peroxide lattice, which is a three-dimensional cubic lattice of coordination number 3. For integer n > 0, these loop models provide…

A statistical model of loops on the three-dimensional lattice is proposed and is investigated. It is O(n)-type but has loop fugacity that depends on global three-dimensional shapes of loops in a particular fashion. It is shown that, despite…

Motivated by recent work that mapped the low-temperature properties of a class of frustrated spin $S=1$ kagome antiferromagnets with competing exchange and single-ion anisotropies to the fully-packed limit (with each vertex touched by…

We explore the phase diagram of the O($n$) loop model on the square lattice in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling.…

The low energy spectrum of a spin chain with $OSp(3|2)$ supergroup symmetry is studied based on the Bethe ansatz solution of the related vertex model. This model is a lattice realization of intersecting loops in two dimensions with loop…

We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with…

Our aim is to give a self-contained review of recent advances in the analytic description of the deconfinement transition and determination of the deconfinement temperature in lattice QCD at large N. We also include some new results, as for…

We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models, by combining Enting's finite lattice method (FLM) with exact transfer matrix enumerations. The models encompass…

The O(n) loop model on the honeycomb lattice with mixed ordinary and special boundary conditions is solved exactly by means of the Bethe ansatz. The calculation of the dominant finite-size corrections to the eigenspectrum yields the mixed…