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Physical review. B, Condensed matter

Exact solution for a one-dimensional chain of hindered dipoles with a transverse tunneling field

Michael W. Klein, Zhong He Wang

Published May 1, 1985• 1 citation
Publisher

Abstract

We consider an infinite chain of four-orientational hindered dipoles with near-neighbor interaction J. The dipoles are allowed to undergo tunneling into the near-neighbor wells (90\ifmmode^\circ\else\textdegree\fi{} tunneling) on the same site. We show that the partition function ${Z}_{D}$(J) of the dipoles is ${Z}_{D}$(J)=${Z}_{S}^{2}$(J/2), where ${Z}_{S}$ is the partition function for a chain of Ising-model spins in a transverse field similar to that treated by Pfeuty. The dipoles act like a pair of independently embedded Ising-spin chains in a transverse field.

DOI
10.1103/physrevb.31.5894

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We study the time dependent behavior of the four-spin interactions Ising chain in the presence of a disordered transverse magnetic field. In order to analyze the effects of field randomness in the dynamical behavior of the system we calculate the time-dependent correlation function and the longitudinal relaxation function of the infinite chain. We consider a bi-modal distribution for the field energy strength, where one of its values equals the exchange coupling energy while the other value can be lower or higher than the coupling energy. We find that an increasing concentration of weaker fields produces an enhancement of the central mode behavior. However, when the concentration of stronger fields increases, the system undergoes a crossover from central mode to collective-type dynamics.