The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T=T_c

The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $$ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix elements of the magnetization operator $sigma(x)$ present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.