Related papers: Critical behaviour of loop models on causal triang…

We extend the 2 dimensional Causal Dynamical Triangulation (CDT) model from the usual model of closed string to the one of open-closed string. The matrix-vector model describing the loop gas model is modified so as to possess the nature of…

A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations $\sim |{\bf x}|^{-a}$ for large separations ${\bf x}$ is given. Directly for three-dimensional systems and different…

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a non-conserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to…

Critical site percolation on the triangular lattice is described by the Yang-Baxter solvable dilute $A_2^{(2)}$ loop model with crossing parameter specialized to $\lambda=\frac\pi3$, corresponding to the contractible loop fugacity…

In this paper we study the annealed coupling of an Ising model with 2-dimensional causal dynamical triangulation model. After a short review of previous results, we prove the existence of the so-called critical line and derive its…

We consider a model of restricted dimers coupled to two-dimensional causal dynamical triangulations (CDT), where the dimer configurations are restricted in the sense that they do not include dimers in regions of high curvature. It is shown…

We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\times n$ square lattice, with the boundary condition for $Z$ depending on two…

Yang-Baxter integrable dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models are considered on the torus in their simplest physical regimes. A combination of boundary conditions $(h,v)$ is applied in the horizontal and vertical directions…

We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model…

For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix $R_{mn}$, whose elements converge to two constants. This allows for an effective extrapolation of the…

In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and…

Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show…

In the usual statistical model of a dense polymer (a single space-filling loop on a lattice) in two dimensions the loop does not cross itself. We modify this by including intersections in which {\em three} lines can cross at the same point,…

We consider a canonical ensemble of dynamical triangulations of a 2-dimensional sphere with a hole where the number $N$ of triangles is fixed. The Gibbs factor is $\exp (-\mu \sum \deg v)$ where $\deg v$ is the degree of the vertex $v$ in…

Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a…

We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio \tau. Loops…

We investigate the disordered copolymer and pinning models, in the case of a correlated Gaussian environment with summable correlations, and when the return distribution of the underlying renewal process has a polynomial tail. As far as the…

Most neural models of causality assume static causal graphs, failing to capture the dynamic and sparse nature of physical interactions where causal relationships emerge and dissolve over time. We introduce the Causal Process Framework and…

We compute lattice correlation functions for the model of critical dense polymers on a semi-infinite cylinder of perimeter $n$. In the lattice loop model, contractible loops have a vanishing fugacity whereas non-contractible loops have a…