Related papers: Macroscopic loops in the loop O(n) model via the X…

We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…

In this paper we study the large N limit of the $O(N)$-invariant linear sigma model, which is a vector-valued generalization of the $\Phi^4$ quantum field theory, on the three dimensional torus. We study the problem via its stochastic…

Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was…

Much recent rigorous study of the classical ferromagnetic Ising model has been powered by its graphical representations, such as the random current and loop O(1) model (high temperature expansion). In this paper, we prove uniqueness of…

It is shown that every tree of size $n$ over a fixed set of $\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\big(\frac{n}{\log_\sigma n}\big) = O\big(\frac{n \log \sigma}{\log n}\big)$ many…

The double dimer model is defined as the superposition of two independent uniformly distributed dimer covers of a graph. Its configurations can be viewed as disjoint collections of self-avoiding loops. Our first result is that in…

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…

We analyze the asymptotic behavior of random variables $x(n,x\_0)$ defined by $x(0,x\_0)=x\_0$ and $x(n+1,x\_0)=A(n)x(n,x\_0)$, where $\sAn$ is a stationary and ergodic sequence of random matrices with entries in the semi-ring…

We study a connection between random tensors and random matrices through $U(\tau)$ matrix models which generate fully packed, oriented loops on random surfaces. The latter are found to be in bijection with a set of regular edge-colored…

An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The…

Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $\sqrt{\log N}$. The level lines of such functions form a loop $O(2)$ model on the edges of the hexagonal…

Loop extrusion convincingly describes how certain Structural Maintenance of Chromosome (SMC) proteins mediate the formation of large DNA loops. Yet, most of the existing computational models cannot reconcile recent in vitro observations…

We present a full two-loop O(g^6) perturbative field theoretic calculation of the expectation value of two circular Maldacena-Wilson loops in D=4 N=4 supersymmetric U(N) gauge theory. It is demonstrated that, after taking into account very…

We study the volume of rigid loop-$O(n)$ quadrangulations with a boundary of length $2p$ in the non-generic critical regime. We prove that, as the half-perimeter $p$ goes to infinity, the volume scales in distribution to an explicit random…

We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…

We present a three-loop O(g^6) calculation of the difference between the expectation values of Wilson loops evaluated in N=4 and superconformal N=2 supersymmetric Yang-Mills theory with gauge group SU(N) using dimensional reduction. We find…

Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts…

We investigate the structure of the macroscopic $n$-loop amplitude obtained from the two-matrix model at the unitary minimal critical point $(m+1,m)$. We derive a general formula for the $n$-resolvent correlator at the continuum planar…

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating…

Given samples from two distributions over an $n$-element set, we wish to test whether these distributions are statistically close. We present an algorithm which uses sublinear in $n$, specifically, $O(n^{2/3}\epsilon^{-8/3}\log n)$,…