Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws

The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the superconducting transition in Ba$_{0.6}$K$_{0.4}$BiO$_3$ and in Bi$_2$Sr$_2$CaCu$_2$O$_8$, there are singularities in higher order derivatives of the free energy. A relation between exponents of different observables has been found, regardless of whether the exponents are classical (mean-field theory, no fluctuations, integer order of a transition) or not (fluctuation effects included). We also comment on the phase transition in a thin film.Comment: 10 pages, no figure

An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.Comment: 7 pages, LaTe

Stationary axisymmetric solutions of five dimensional gravity

We consider stationary axisymmetric solutions of general relativity that asymptote to five dimensional Minkowski space. It is known that this system has a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers-Perry black hole starting from the Schwarzschild solution in five dimensions.Comment: 31 pages, LaTeX; references adde