Related papers: Connecting Complex Electronic Pattern Formation to…
Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
Despite great progress in the study of critical percolation on $\mathbb{Z}^d$ for $d$ large, properties of critical clusters in high-dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions.…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…
We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to, the critical temperature. In a regime where the temperature approaches the critical point and, simultaneously, the…
To investigate the properties of $c=1$ matter coupled to $2$d{--}gravity we have performed large-scale simulations of two copies of the Ising Model on a dynamical lattice. We measure spin susceptibility and percolation critical exponents…
We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites…
We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…
For the 2D Ising model, we analyzed dependences of thermodynamic characteristics on number of spins by means of computer simulations. We compared experimental data obtained using the Fisher-Kasteleyn algorithm on a square lattice with…
The isothermal compressibility of a general crystal is analyzed within classical density functional theory. Our approach can be used for homogeneous and unstrained crystals containing an arbitrarily high density of local defects. We start…
We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its…
Extensive simulations are made on the bimodal Ising Spin Glass (ISG) in dimension four. The transition temperature is established using a combination of standard finite size scaling and of thermodynamic derivative peak data. Measurements in…
Under some general assumptions, we construct the scaling limit of open clusters and their associated counting measures in a class of two dimensional percolation models. Our results apply, in particular, to critical Bernoulli site…
In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…
We performed a high statistics simulation of Ising spins coupled to 2D quantum gravity on toroidal geometries. The tori were triangulated using the Regge calculus approach and contained up to $512^2$ vertices. We used a constant area…
We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for…
Although the physical properties of the 2D and 1D Ising models are quite different, we point out an interesting connection between their complex-temperature phase diagrams. We carry out an exact determination of the complex-temperature…