Related papers: Method for estimating critical exponents in percol…
We have generalized the idea of backbend in a nearest-neighbor oriented bond percolation process by considering a backbend sequence $\beta : \mathbb{Z}_+ \to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $\beta$-backbend path from the…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent…
Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in $d$-space, with distance parameter $r$ and intensities $\lambda,\mu$. For any $\lambda>0$ we consider the percolation…
We present an extension of the so-called cumulant crossing method which is used for determination of critical point in Monte Carlo simulations.The new method uses linear combination of several different order-parameter moments and almost…
We present a detailed description of the idea and procedure for the newly proposed Monte Carlo algorithm of tuning the critical point automatically, which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and Y. Okabe,…
We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents…
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…
Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
We study the two and four dimensional Nishimori multicritical point via high temperature expansions for the $\pm J$ distribution, random-bond, Ising model. In $2d$ we estimate the the critical exponents along the Nishimori line to be…
We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all…
The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we…
In the bond percolation model on a lattice, we colour vertices with $n_c$ colours independently at random according to Bernoulli distributions. A vertex can receive multiple colours and each of these colours is individually observable. The…
We investigate the critical behavior of continuous phase transitions in the context of Ginzburg Landau models with a double well effective potential. In particular, we show that the recently proposed configurational entropy, a measure of…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We consider bond and site Bernoulli Percolation in both the oriented and the non-oriented cases on $\mathbb{Z}^d$ and obtain rigorous upper bounds for the critical points in those models for every dimension $d \geq 3$.
Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we…
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is…