Multi-spin-flip dynamics of the Ising chain

Two kinds of multi-spin-flip discrete-time dynamics of the Ising chain are solved analytically. One dynamics is the two sublattice type flip and each sublattice contains n sequential spins alternately. The other has the overlapped multi-spin-flip sequence. The state of n spins at the next time step is selected from 2n states using the heat-bath type transition probability. These dynamics of the Ising chain are equivalent to the statics of the square-lattice Ising model with a 1 × 2 unit cell or of the triangular-lattice Ising model. The analytic solutions of the single spin relaxation time of these dynamics are obtained using these equivalences.