相关论文: On the universality of compact polymers

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…

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…

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)…

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…

We present a Markov-chain Monte Carlo algorithm of "worm"type that correctly simulates the O(n) loop model on any (finite and connected) bipartite cubic graph, for any real n>0, and any edge weight, including the fully-packed limit of…

We exhibit the multicritical phase structure of the loop gas model on a random surface. The dense phase is reconsidered, with special attention paid to the topological points $g=1/p$. This phase is complementary to the dilute and higher…

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 physical properties of 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.…

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 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…

We study a classical model of fully-packed loops on the square lattice, which interact through attractive loop segment interactions between opposite sides of plaquettes. This study is motivated by effective models of interacting quantum…

Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop having a fugacity of n. We study such loops subjected to a particular kind of staggered field w, which for n -> infinity has the…

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple…

Exact results for conformational statistics of compact polymers are derived from the two-flavour fully packed loop model on the square lattice. This loop model exhibits a two-dimensional manifold of critical fixed points each one…

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.…

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…

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…

Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of self-assembled rigid rods on triangular and honeycomb lattices at intermediate density has been studied. The system is composed of monomers with two…

We investigate the O($n$) nonintersecting loop model on the square lattice under the constraint that the loops consist of ninety-degree bends only. The model is governed by the loop weight $n$, a weight $x$ for each vertex of the lattice…

We derive the exact critical couplings ($x^*, y_{\rm a}^*$), where $y_{\rm a}^*/x^* = \sqrt{1+\sqrt2} = 1.533\ldots\,$, for the polymer adsorption transition on the honeycomb lattice, along with the universal critical exponents, from the…