Related papers: Geometric Exponents, SLE and Logarithmic Minimal M…
These lecture notes provide a (almost) self-contained account on conformal invariance of the planar critical Ising and FK-Ising models. They present the theory of discrete holomorphic functions and its applications to planar statistical…
We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}. We study the random sets of points at which the curve…
We present a mathematical proof of theoretical predictions made by Arguin and Saint-Aubin, as well as by Bauer, Bernard, and Kytola, about certain non-local observables for the two-dimensional Ising model at criticality by combining…
The interplay of topological constraints and persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three dimensional lattice model. We ask if the results are consistent with…
We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like…
In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied,…
In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic 2D Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo…
The conformal loop ensemble (CLE) is a conformally invariant random collection of loops. In the non-simple regime $\kappa'\in (4,8)$, it describes the scaling limit of the critical Fortuin-Kasteleyn (FK) percolations. CLE percolations were…
We provide an explicit construction of finite 4-regular graphs $(\Gamma_k)_{k\in \mathbb N}$ with ${girth \Gamma_k\to\infty}$ as $k\to\infty$ and $\frac{diam \Gamma_k}{girth \Gamma_k}\leqslant D$ for some $D>0$ and all $k\in\mathbb{N}$. For…
The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein {\it et…
The result of 2-dimensional Gaussian lattice fit to a speckle intensity pattern based on a linear model that includes nearest-neighbor interactions is presented. We also include a Monte Carlo simulation of the same spatial speckle pattern…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a…
Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy $F$ is measured as a…
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to…
Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies…
We derive boundary arm exponents for SLE. Combining with the convergence of critical lattice models to SLE, these exponents would give the alternating half-plane arm exponents for the corresponding lattice models.
Using a lattice-based Monte Carlo code for simulating self-avoiding flexible polymers in three dimensions in the absence of explicit hydrodynamics, we study their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected to…
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of zero external magnetic field, using a generalization of the combinatorial method of Feynman and…
We discuss analytical approximation schemes for the dynamics of diluted spin models. The original dynamics of the complete set of degrees of freedom is replaced by a hierarchy of equations including an increasing number of global…