Abstract
The author presents a statistical mechanical analysis for a one-dimensional lattice gas in which the pair interaction potential is exponential and repulsive of Kac type phi (x)= alpha exp(- gamma mod x mod ) with alpha >0. mod x mod >0 (this analysis is complementary to the one studied by Newman (1964) for a one-dimensional fluid). The main objectives of this work are the following. First, the author derives an analytical expression (in the weak long-range limit, gamma to 0) for the traces and the maximum eigenvalues of the Kac operators. Second, the author derives the equation of state for the repulsive lattice gas in the weak long-range limit. Furthermore, the author mentions the possibility of the application of this model to study classical problems in biophysics. Third, the author finds interesting properties for the non-Hermitian Kac operator which suggest that the spanning property for this operator is possible.
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