Free energy on a cycle graph and trigonometric deformation of heat kernel traces on odd spheres. (English) Zbl 1387.35321
Summary: 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.
MSC:
| 35K08 | Heat kernel |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 05C38 | Paths and cycles |
| 82B30 | Statistical thermodynamics |
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