Finite size effects in the thermodynamics of a free neutral scalar field

Abstract

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.

9 figures, accepted for publication

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Cited by in corpus (4)

• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• Phase transition for the system of small volume in the ${\varphi }^4$ theory in the Tsallis nonextensive statistics
• Scaled variables and the quark-hadron duality
• The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies