Abstract
A one-dimensional lattice gas model with the nearest-neighbor and the next-nearest-neighbor interaction is exactly solved. If the nearest-neighbor interaction(£) is repulsive or attractive with the repulsive next-nearest-neighbor interaction (TJ>-c/2), the coefficient of thermal expansion has negative regions. Recently the negative thermal expansion of one-dimensional fluids has been studied by several authors. 1 H> In a preceding paper 1 > a one-dimensional lattice gas model with the hard-core nearest-neighbor and the next-nearest-neighbor interaction was exactly solved. In the case of the repulsive next-nearest-neighbor interaction, the coefficient of thermal expansion has a negative region, and hence there is an intersection of isotherms and a maximum number density as a function of tempera ture in the constant pressure process. In the present paper, the one-dimensional lattice gas with the nearest-neighbor interaction and the next-nearest-neighbor interaction is solved exactly. We investi gate the properties of the coefficient of thermal expansion. If the interactions are repulsive, there are three regions in which the coefficient of thermal expansion is negative. We consider a lattice gas on a one-dimensional lattice ofM lattice sites. We assume that the interaction energies between nearest- and next-nearest-neighbor particles in the gas are given by c and 7}, respectively. By using the transfer matrix method, 4 J,s> it wa:s shown 1 > that the eigenvalues of the transfer matrix are determined
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