Free Energy on a Cycle Graph and Trigonometric Deformation of Heat   Kernel Traces on Odd Spheres
  We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified Bessel functions, we obtain the values of the free energies after a suitable regularization. 
Nahomi Kan (NIT, Gifu College) and Kiyoshi Shiraishi (Yamaguchi   University)
math-ph hep-th math.MP