相关论文: Self Avoiding Surfaces in the 3D Ising Model

We systematically investigate the self-assembly of anisotropic cone-shaped particles decorated by ring-like attractive patches. We demonstrate that the self-assembled clusters, which arise due to the conical particle's anisotropic shape…

We propose a computational methodology based on a hierarchical cluster growth process to solve spin-3/2 Ising models efficiently. The method circumvents the exponential complexity (\(4^{N}\)) of the canonical ensemble partition function by…

In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…

A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly…

We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the…

We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…

The deconfinement transition in SU(2) gauge theory and the magnetization transition in the Ising model belong to the same universality class. The critical behaviour of the Ising model can be characterized either as spontaneous breaking of…

We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the…

The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. If the phase transition of the model is second order, it can be equivalently described as a percolation transition of…

In (the surface of) a convex polytope P^3 in R^4, an area-minimizing surface avoids the vertices of P and crosses the edges orthogonally. In a smooth Riemannian manifold M with a group of isometries G, an area-minimizing G-invariant…

The paper concerns clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis…

The emergence of order and geometric limit shapes in a three-dimensional (3D) Coulomb phase subject to domain wall boundary conditions (DWBC) is investigated. While the arctic circle phenomenon -- the spatial segregation of frozen and…

In this paper we establish some relations between percolation on a given graph G and its geometry. Our main result shows that, if G has polynomial growth and satisfies what we call the local isoperimetric inequality of dimension d > 1, then…

We show that for all p>p_c(\Z^d) percolation parameters, the probability that the cluster of the origin is finite but has at least t vertices at distance one from the infinite cluster is exponentially small in t. We use this to give a short…

We study a percolation problem on a substrate formed by two-dimensional XY spin configurations, using Monte Carlo methods. For a given spin configuration we construct percolation clusters by randomly choosing a direction $x$ in the spin…

Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies or interstellar molecular clouds. We study the origin of these properties…

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…

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…

Probabilities of crossing on same-spin clusters, seen as order parameters, have been introduced recently for the critical 2d Ising model by Langlands, Lewis and Saint-Aubin. We extend Cardy's ideas, introduced for percolation, to obtain an…

In this PhD thesis we develop the frame work of triple crossing diagram maps (TCD maps), which describes constrained configurations of points in projective spaces and discrete dynamics on these configurations. We are able to capture the…