A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at θ=π\theta=\pi

In this work we study the two and three-dimensional antiferromagnetic Ising model with an imaginary magnetic field $i\theta$ at $\theta=\pi$. In order to perform numerical simulations of the system we introduce a new geometric algorithm not affected by the sign problem. Our results for the $2D$ model are in agreement with the analytical solutions. We also present new results for the $3D$ model which are qualitatively in agreement with mean-field predictions

Multiple merging in the Abell cluster 1367

We present a dynamical analysis of the central ~1.3 square degrees of the cluster of galaxies Abell 1367, based on 273 redshift measurements (of which 119 are news). From the analysis of the 146 confirmed cluster members we derive a significantly non-Gaussian velocity distribution, with a mean location C_{BI} = 6484+/-81 km/s and a scale S_{BI} = 891+/-58 km/s. The cluster appears elongated from the North-West to the South-East with two main density peaks associated with two substructures. The North-West subcluster is probably in the early phase of merging into the South-East substructure (~ 0.2 Gyr before core crossing). A dynamical study of the two subclouds points out the existence of a group of star-forming galaxies infalling into the core of the South-East subcloud and suggests that two other groups are infalling into the NW and SE subclusters respectively. These three subgroups contain a higher fraction of star-forming galaxies than the cluster core, as expected during merging events. Abell 1367 appears as a young cluster currently forming at the intersection of two filaments.Comment: 15 pages, 13 figures, 7 tables. Accepted for publication on A&A. High resolution figures at http://goldmine.mib.infn.it/papers/a1367.htm

A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. (i) Every cluster and every co-cluster (complement of a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing edges. Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. On one hand, this gives rise to a bunch of new open problems related to c-planarity, on the other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $\alpha$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.Comment: 25 pages, 4 figures, 8 table

The phase transitions in 2D Z(N) vector models for N>4

We investigate both analytically and numerically the renormalization group equations in 2D Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index \nu\ is computed. For N=7, 17 the critical points are located by Monte Carlo simulations and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.Comment: 19 pages, 8 figures, 10 tables; version to appear on Phys. Rev.