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Register a new userOne-dimensional Ising model with multispin interactions
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L. Turban
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We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions (BC) and we calculate the two-spin correlation function. When placed in an external field $H$ the system is shown to be self-dual. Using another change of spin variables the one-dimensional (1D) Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions $K$ and $H$. The 2D system, with size $mtimes N/m$, has the topology of a cylinder with helical BC. In the thermodynamic limit $N/mtoinfty$, $mtoinfty$, a 2D critical singularity develops on the self-duality line, $sinh 2Ksinh 2H=1$.
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The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as $K_{i}$ increase, especially when $K_{i}>J_{i}/2$ ($J_{i}$ and $K_{i}$ are exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak ($K_{i}<J_{i}/2$).
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