Finite size effects in the thermodynamics of a free neutral scalar field on the lattice and in the continuum

Abstract

The thermodynamic properties of the free neutral scalar field given in the framework of the method of the path integral quantization both on the lattice and in the continuum limit were investigated. It was revealed that the trace anomaly enhancement for the free massive neutral scalar field at low temperature and small volume is a consequence of the thermodynamic inconsistency of the model both on the lattice and in the continuum limit. It was also found that the statistical formalism for the free massive neutral scalar field on the finite lattice is thermodynamically inconsistent in all range of the variables of state \(T\) and \(V\) including the thermodynamic limit. However, in the continuum limit the statistical formalism for the free massive neutral scalar field is thermodynamically self-consistent only in the thermodynamic limit or at high temperatures.