Potts Models with (17) Invisible States on Thin Graphs

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.Comment: (2) Minor typos corrected, references update

The Gonihedric Ising Model and Glassiness

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum. In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to investigation of the non-equilibrium, glassy behaviour of the model.Comment: To appear as Chapter 7 in Rugged Free-Energy Landscapes - An Introduction, Springer Lecture Notes in Physics, 736, ed. W. Janke, (2008

Emission Measures and Emission-measure-weighted Temperatures of Shocked ISM and Ejecta in Supernova Remnants

A goal of supernova remnant (SNR) evolution models is to relate fundamental parameters of a supernova (SN) explosion and progenitor star to the current state of its SNR. The SNR hot plasma is characterized by its observed X-ray spectrum, which yields electron temperature, emission measure and abundances. Depending on their brightness, the properties of the plasmas heated by the SNR forward shock, reverse shock or both can be measured. The current work utilizes models which are spherically symmetric. One dimensional hydrodynamic simulations are carried out for SNR evolution prior to onset of radiative losses. From these, we derive dimensionless emission measures and emission-measure-weighted temperatures, and we present fitting formulae for these quantities as functions of scaled SNR time. These models allow one to infer SNR explosion energy, circumstellar medium density, age, ejecta mass and ejecta density profile from SNR observations. The new results are incorporated into the SNR modelling code SNRPy. The code is demonstrated with application to three historical SNRs: Kepler, Tycho and SN1006.Comment: 50 pages, 10 figures, 5 table