Susceptibility of the one-dimensional Ising model: is the singularity at T = 0 an essential one?

James H. Taylor

Published 2020-01-06Version 1

The zero-field, isothermal susceptibility of the classical one-dimensional Ising model is shown to have a relatively simple singularity as the temperature approaches zero, proportional only to the inverse temperature. This is in contrast to what is seen throughout the literature: an essential singularity involving an exponential dependence on the inverse temperature. The analysis involves nothing beyond straightforward series expansions, starting either with the partition function for a closed chain in a magnetic field, obtained using the transfer matrix approach; or from the expression for the zero-field susceptibility found via the fluctuation-dissipation theorem. In both cases, the exponential singularity is cancelled by part of a term that is usually considered ignorable in the thermodynamic limit.