Related papers: Wrapping probabilities for Potts spin clusters on …
Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive…
The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
The analysis of extensive numerical data for the percolation probabilities of incipient spanning clusters in two dimensional percolation at criticality are presented. We developed an effective code for the single-scan version of the…
Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in…
The spontaneous symmetry breaking in the Ising model can be equivalently described in terms of percolation of Wolff clusters. In O(n) spin models similar clusters can be built in a general way, and they are currently used to update these…
We report a transfer matrix study of the random bond $q-$state Potts model in the vicinity of the Ising model $q=2$. We draw attention to a precise determination of magnetic scaling dimensions in order to compare with perturbative results.…
We investigated numerically an Ising model coupled to two-dimensional Euclidean gravity with spherical topology, using Regge calculus with the $dl/l$ path-integral measure to discretize the gravitational interaction. Previous studies of…
We obtain the harmonic measure of the hulls of critical percolation clusters and Ising-model Fortuin-Kastelyn clusters using a biased random-walk sampling technique which allows us to measure probabilities as small as 10^{-300}. We find the…
In this article we create a new algorithm for the perfect simulation of the infinite Potts model at a sufficiently small or at a sufficiently high temperature, in particular under the transition phase temperature. We study the model for…
We derive three critical exponents for Bernoulli site percolation on the on the Uniform Infinite Planar Triangulation (UIPT). First we compute explicitly the probability that the root cluster is infinite. As a consequence, we show that the…
We prove a Torres-like formula for the $L^2$-Alexander torsions of links, as well as formulas for connected sums and cablings of links. Along the way we compute explicitly the $L^2$-Alexander torsions of torus links inside the three-sphere,…
We present an analysis leading to precise locations of the multicritical points for spin glasses on regular lattices. The conventional technique for determination of the location of the multicritical point was previously derived using a…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
We describe a method to estimate R\'enyi entanglement entropy of a spin system, which is based on the replica trick and generative neural networks with explicit probability estimation. It can be extended to any spin system or lattice field…
We study infinite ``$+$'' or ``$-$'' clusters for an Ising model on an connected, transitive, non-amenable, planar, one-ended graph $G$ with finite vertex degree. If the critical percolation probability $p_c^{site}$ for the i.i.d.~Bernoulli…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Using the random-cluster representation of the $q$-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings $K$ and number of states per spin $q$. Proper combination of…
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two…
A Fortuin-Kasteleyn cluster on a torus is said to be of type $\{a,b\}, a,b\in\mathbb Z$, if it possible to draw a curve belonging to the cluster that winds $a$ times around the first cycle of the torus as it winds $-b$ times around the…