相关论文: Macroscopic loops in the loop O(n) model via the X…

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…

Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative…

We explore the properties of the low-temperature phase of the O($n$) loop model in two dimensions by means of transfer-matrix calculations and finite-size scaling. We determine the stability of this phase with respect to several kinds of…

We study the fractal geometry of O($n$) loop configurations in two dimensions by means of scaling and a Monte Carlo method, and compare the results with predictions based on the Coulomb gas technique. The Monte Carlo algorithm is applicable…

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…

We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking…

We reformulate the O(N) sigma model as a loop model whose configurations are the all-order strong coupling graphs of the original model. The loop configurations are represented by a pointer list in the computer and a Monte Carlo update…

We continue our investigation of the nested loop approach to the O(n) model on random maps, by extending it to the case where loops may visit faces of arbitrary degree. This allows to express the partition function of the O(n) loop model as…

We prove the existence of macroscopic loops in the loop O(2) model with $\frac12\leq x^2\leq 1$ or, equivalently, delocalisation of the associated integer-valued Lipschitz function on the triangular lattice. This settles one side of the…

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.…

In search of non-trivial field theories in high dimensions, we study further the tensor representation of the $O(N)$-symmetric $\phi^4$ field theory introduced by Herbut and Janssen (Phys. Rev. D. 93, 085005 (2016)), by using four-loop…

We show how to compute the probability distributions of the order parameter of the $O(n)$ model at two-loop order of perturbation theory generalizing the methods developed for computing the same in case of the Ising model…

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…

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…

In the O(n) loop model on random planar maps, we study the depth - in terms of the number of levels of nesting - of the loop configuration, by means of analytic combinatorics. We focus on the 'refined' generating series of pointed disks or…

We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor…

Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that…

The Landau-Wilson field theory with $O(n)\times O(m)$ symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in $4 - \varepsilon$ dimensions within the minimal…

We present a family of graphical representations for the O($N$) spin model, where $N \ge 1$ represents the spin dimension, and $N=1,2,3$ corresponds to the Ising, XY and Heisenberg models, respectively. With an integer parameter $0 \le \ell…

Pure gauge theories can be formulated in terms of Wilson Loops correlators by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator,…