On the Singularity of Dynamical Response and Critical Slowing Down

Phenomenological arguments on the critical slowing down is presented and “similarity law” is proposed on the indices of the critical slowing down. The similarity law is confirmed in linear spin chains near the critical field and in the kinetic Ising model near the critical temperature. It is exactly shown in the linear spin chains that the critical index of slowing down is different from that of the static susceptibility and that the dynamical susceptibility has a logarithmic singularity with respect to the frequency at the critical field and at zero temperature.