We propose a relationship between thermodynamic phase transitions and groundstate quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and exceptional points of a quantum Hamiltonian in the complexextended parameter space. This approach is applied in the interacting boson model,...

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increase...

We calculate the fluctuation of the energy of a system in Tsallis statistics following the finite heat bath canonical ensemble approach. We obtain this fluctuation as the second derivative of the logarithm of the partition function plus an additional term. We also find an explicit expression for the relative fluctuation as related to the number of degrees of freedom of the bath and the composit...

In this article we consider the Picard group SL(2, Z[;']), viewed as a discrete subgroup of the isometries of hyperbolic space. We fix a canonical choice of generators and then construct a Markov partition for the action of the group on the sphere at infinity. Our main application is to the study of the zeta function associated to the associated three-dimensional hyperbolic manifold.

The statistical consequences of minimal length supposition are investigated for a canonical ensemble of ideal gas. These effects are encoded in the so-called Generalized Uncertainty Principle (GUP) of the second order. In the frame work of the considered GUP scenario, a unique partition function is obtained by using of two different methods of quantum and classical approaches. It should be noti...

Abstract We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit...

We describe a new algorithm that approaches Monte Carlo simulation in statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to directly extract an estimate for the density of states. The canonical probability can then be found at any temperature by weighting by the appropriate Boltzmann factor,...

We look at the Yang-Lee zeros in the complex temperature plane of Bose-Einstein condensate in a harmonic trap of dimensions 2− 5. We apply the Grossmann classification scheme to characterize the phase transition. We observe how the true phase transition is approached in the infinite particle number limit. We find the scaling with respect to particle number of the imaginary part of the zero of t...

The electronic partition function for the hydrogen atom is derived by integration over the recently-available Coulomb propagator. This provides a resolution to an old paradox in statistical mechanics: the apparent divergence of the hydrogen partition function. Electronic excitation does not contribute significantly to the standard-state partition function until temperatures of the order of 5000...

We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the authors in Prog. Theor. Phys. 111, 661 (2004). The expression can be handled both analytically and numerically, which is useful for examining how the analyticit...