The divergence of the partition function of the attractive Frisch-Lloyd model of disordered systems

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Abstract
The path-integral method is used to calculate the partition function of a particle moving in a one-dimensional Frisch-Lloyd disordered system. It is found that the partition function is divergent. The fact that the partition function does not exist for this model disordered system therefore implies that the famous Frisch-Lloyd model for attractive potentials does not represent a stable Boltzmann system. A physical argument for the causes of divergence is outlined.