Related papers: The O(n) loop model on the 3-12 lattice

We derive the exact critical line of the O($n$) loop model on the martini lattice as a function of the loop weight $n$.A finite-size scaling analysis based on transfer matrix calculations is also performed.The numerical results coincide…

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 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…

In the loop $O(n)$ model a collection of mutually-disjoint self-avoiding loops is drawn at random on a finite domain of a lattice with probability proportional to $${\lambda^{\# \mbox{edges}} n^{\# \mbox{loops}},}$$ where $\lambda, n \in…

We study the O(N) loop model on the Honeycomb lattice with real value $N \geq 1$ by means of a cluster algorithm. The formulation of the algorithm is based on the equivalence of the O(N) loop model and the low-temperature graphical…

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…

The classical spin $O(n)$ model is a model on a $d$-dimensional lattice in which a vector on the $(n-1)$-dimensional sphere is assigned to every lattice site and the vectors at adjacent sites interact ferromagnetically via their inner…

We study the $O(n)$ loop model on the honeycomb lattice with open boundary conditions. Reflection matrices for the underlying Izergin-Korepin $R$-matrix lead to three inequivalent sets of integrable boundary weights. One set, which has…

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…

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…

An efficient algorithm is presented to simulate the O(N) loop model on the square lattice for arbitrary values of $N>0$. The scheme combines the worm algorithm with a new data structure to resolve both the problem of loop crossings and the…

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…

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 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.…

A relation between the average length of loops and their free energy is obtained for a variety of O(n)-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number)…

We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer $n\ge 3$. Using the exact renormalization group method we have been able to obtain…

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…

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…

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the…

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we study a similar anisotropic spin-1/2 Heisenberg model on…