Ruppeiner geometry of anyon gas

Thermodynamic geometry of spin-one lattice models. I. Spin and quadrupolar orders and critical scaling functions in one dimension

State space Riemannian geometry is obtained for the one-dimensional Blume-Emery-Griffiths model and its Blume-Capel and Griffiths model limits, and its (pseudo)critical as well as noncritical parameter regimes are extensively investigated. Two codimension one geometries are obtained by taking suitable hypersurfaces in the three-dimensional state space manifold, and the induced thermal metrics are accordingly interpreted in terms of constrained fluctuations. The three-dimensional scalar curvature and the two two-dimensional curvatures are shown to be consistent with Ruppeiner's conjecture relating the inverse of the singular free energy to the thermodynamic scalar curvature. Moreover, they are found to be in an excellent agreement over a greater part of the noncritical region with the corresponding correlation lengths for the spin and the quadrupolar order parameters. The scaling function for the free energy near the pseudocritical and tricritical points is obtained thermodynamically by using Ruppeiner's conjecture. A connection is made between the sign change in the curvatures and the change in fluctuation patterns of the order parameters. In the accompanying paper we shall analyze the geometry of the spin-one model in its mean field approximation.

Perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases

We investigate perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by a nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive one may be divided to two different regimes. According to the deviation parameter of the system to the nonextensive case, one can find a special value of fugacity, z^{*}, where the sign of thermodynamic curvature is changed. Therefore, we argue that the nonextensive parameter induces an attractive (repulsive) statistical interaction for z<z^{*} (z>z^{*}) for an ideal classical gas. Also, according to the singular point of thermodynamic curvature, we consider the condensation of nonextensive Boson gas.

Condensation of an ideal gas obeying non-Abelian statistics

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.

Thermodynamic geometry of fractional statistics

We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the nonrelativistic and ultrarelativistic limits. Also, two other fractional statistics, namely, Gentile and Polychronakos fractional statistics, will be considered and similarities and differences between these statistics will be explored. Thermodynamic geometry suggests that a two dimensional Haldane fractional exclusion gas is more stable than higher dimensional gases. Also, a complete picture of attractive and repulsive statistical interaction of fractional statistics is given. For a special kind of fractional statistics, by considering the singular points of thermodynamic curvature, we find a condensation for a nonpure bosonic system which is similar to the Bose-Einstein condensation and the phase transition temperature will be worked out.

Nonperturbative thermodynamic geometry of anyon gas

Following our earlier work on the Ruppeiner geometry of an anyon gas [B. Mirza and H. Mohammadzadeh, Phys. Rev. E 78, 021127 (2008)], we will derive nonperturbative thermodynamic curvature of a two-dimensional ideal anyon gas. At different values of the thermodynamic parameter space, some unique and interesting behaviors of the anyon gas are explored. A complete picture of attractive and repulsive phases of the anyon gas is given.