Nonequilibrium ionization states and cooling rates of the photoionized enriched gas

Nonequilibrium (time-dependent) cooling rates and ionization state calculations are presented for low-density gas enriched with heavy elements (metals) and photoionized by external ultraviolet/X-ray radiation. We consider a wide range of gas densities and metallicities and also two types of external radiation field: a power-law and the extragalactic background spectra. We have found that both cooling efficiencies and ionic composition of enriched photoionized gas depend significantly on the gas metallicity and density, the flux amplitude, and the shape of ionizing radiation spectrum. The cooling rates and ionic composition of gas in nonequilibrium photoionization models differ strongly (by a factor of several) from those in photoequilibrium due to overionization of the ionic states in the nonequilibrium case. The difference is maximal at low values of the ionization parameter and similar in magnitude to that between the equlibrium and nonequilibrium cooling rates in the collisionally controlled gas. In general, the nonequilibrium effects are notable at T\simlt 10^6 K. In this temperature range, the mismatch of the ionic states and their ratios between the photoequilibrium and the photo-nonequilibrium models reach a factor of several. The net result is that the time-dependent energy losses due to each chemical element (i.e. the contributions to the total cooling rate) differ singificantly from the photoequilibrium ones. We advocate the use of nonequilibrium cooling rates and ionic states for gas with near-solar (and above) metallicity exposed to an arbitrary ionizing radiation flux. We provide a parameter space (in terms of temperature, density, metallicity and ionizing radiation flux), where the nonequilibrium cooling rates are to be used. (abridged)Comment: 14 pages, 11 figures, accepted to MNRA

The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model

In this paper a method previously employed by Salmhofer to establish an exact equivalence of the one-flavour strong coupling lattice Schwinger model with Wilson fermions to some 8-vertex model is applied to the case with two flavours. As this method is fairly general and can be applied to strong coupling QED and purely fermionic models with any (sufficiently small) number of Wilson fermions in any dimension the purpose of the present study is mainly a methodical one in order to gain some further experience with it. In the paper the vertex model equivalent to the two-flavour strong coupling lattice Schwinger model with Wilson fermions is found. It turns out to be some modified 3-state 20-vertex model on the square lattice, which can also be understood as a regular 6-state vertex model. In analogy with the one- flavour case, this model can be viewed as some loop model.Comment: 22 pages LaTe

Antiferromagnetic chain with alternating interactions and megnetic moments

It is shown that for alternating XY chains xzz have two singularities at different values of the applied magnetic field

Spontaneous Magnetization of the Integrable Chiral Potts Model

We show how $Z$-invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrable eigenvectors. When the distance between the two spins in the correlation function becomes infinite it becomes the square of the order parameter. In this way, we show that the spontaneous magnetization can be expressed in terms of the inner products of the eigenvectors of the $N$ asymptotically degenerate maximum eigenvalues. Using our previous results on these eigenvectors, we are able to obtain the order parameter as a sum almost identical to the one given by Baxter. This gives the known spontaneous magnetization of the chiral Potts model by an entirely different approach.Comment: LaTeX 2E document, using iopart.cls with iopams packages, 22 pages, 1 eps figure. Presented at the Simons Center for Geometry and Physics Workshop on Correlation Functions for Integrable Models 2010: January 18-22, 2010. Version 2: The identity conjectured in version 1 is now proved and its proof is presented in arXiv:1108.4713; various small corrections and improvements have been made als