Does the string hypothesis hold for the calculation of thermodynamical quantities?

Abstract

Without using the string hypothesis, we have obtained the large c series expansion of the magnetization and pressure for the nonlinear Schrödinger model of spin- 1 2 particles from the quantum Gel'fand-Levitan equations. On comparison with the results of Lai based on the string hypothesis for the Bethe ansatz solutions, we found that they coincide only in the infinite coupling limit and deviate from each other in the next term of order O(1/ c).