Phase diagram of Nambu-Jona-Lasinio model with dimensional regularization

We investigate the phase diagram on temperature-chemical potential plane in the Nambu-Jona-Lasinio model with the dimensional regularization. While the structure of the resulting diagram shows resemblance to the one in the frequently used cutoff regularization, some results of our study indicate striking difference between these regularizations. The diagram in the dimensional regularization exhibits strong tendency of the first order phase transition.Comment: 9 pages, 9 figure

Conservation Laws in Cellular Automata

If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F if G is constant under the action of F. We characterize such `conservation laws' in several ways, deriving both theoretical consequences and practical tests, and provide a method for constructing all one-dimensional CA exhibiting a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To appear in Nonlinearity. (v2) minor changes/corrections; new references added to bibliograph

Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies. II. comparison of covariant formalisms

We study a covariant formalism for the Sunyaev-Zeldovich effects developed in the previous papers by the present authors, and derive analytic expressions for the redistribution functions in the Thomson approximation. We also explore another covariant formalism recently developed by Poutanen and Vurm. We show that the two formalisms are mathematically equivalent in the Thomson approximation which is fully valid for the cosmic microwave background photon energies. The present finding will establish a theoretical foundation for the analysis of the Sunyaev-Zeldovich effects for the clusters of galaxies.Comment: Accepted version, 7 pages, 1 figure, accepted by Physical Review D for publicatio

Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. IV. Analytic fitting formula for the Numerical Results

We present an accurate analytic fitting formula for the numerical results for the relativistic corrections to the thermal Sunyaev-Zel'dovich effect for clusters of galaxies. The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation. The fitting is carried out for the ranges 0.02 < theta_{e} < 0.05 and 0 < X < 20, where theta_{e} = k_{B}T_{e}/m_{e}c^{2}, X = omega/k_{B}T_{0}, T_{e} is the electron temperature, omega is the angular frequency of the photon, and T_{0} is the temperature of the cosmic microwave background radiation. The accuracy of the fitting is generally better than 0.1%. The present analytic fitting formula will be useful for the analyses of the thermal Sunyaev-Zel'dovich effect for high-temperature galaxy clusters.Comment: 11 pages + 1 table + 2 figures, LaTeX with AASMS macro. Accepted by Astrophysical Journal for publicatio