Pseudo-one-dimensional kinetic Ising model

A simple kinetic model of the weakly coupled linear Ising chains is treated. The $\overrightarrow{\mathrm{q}}$-dependent dynamical susceptibility is obtained, introducing the interchain molecular field into exact one-dimensional solutions. The usual molecular-field-type critical slowing down as $T\to T_c$ is accompanied by an additional noncritical, highly anisotropic slowing down due to high-intrachain short-range order. For the $\overrightarrow{\mathrm{q}}=0\mathrm{}$ mode the factor of the one-dimensional slowing down goes with decreasing temperature as the square of the one-dimensional correlation length. In the case of a strong anisotropy ($J_{\parallel }\gg J_{\perp }$), this factor surpasses the value of the ratio $\frac{J_{\parallel }}{J_{\perp }}$ already well above $T_c$.