Title: Unusual thermodynamics on the fuzzy 2-sphere
Abstract: Higher spin Dirac operators on both the continuum sphere(S 2) and its fuzzy analog(S F 2 ) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is especially true even for the case of integer-spin Dirac operators. Motivated by this feature of the spectrum of a spin 1 Dirac operator on S F 2 , we assume the spin 1 particles obey Fermi-Dirac statistics. This choice is inspite of the lack of a well defined spin-statistics relation on a compact surface such as S 2. The specific heats are computed in the cases of the spin $ \frac{1}{2} $ and spin 1 Dirac operators. Remarkably the specific heat for a system of spin $ \frac{1}{2} $ particles is more than that of the spin 1 case, though the number of degrees of freedom is more in the case of spin 1 particles. The reason for this is inferred through a study of the spectrums of the Dirac operators in both the cases. The zero modes of the spin 1 Dirac operator is studied as a function of the cut-off angular momentum L and is found to follow a simple power law. This number is such that the number of states with positive energy for the spin 1 and spin $ \frac{1}{2} $ system become comparable. Remarks are made about the spectrums of higher spin Dirac operators as well through a study of their zero-modes and the variation of their spectrum with degeneracy. The mean energy as a function of temperature is studied in both the spin $ \frac{1}{2} $ and spin 1 cases. They are found to deviate from the standard ideal gas law in 2+ 1 dimensions.