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The European Physical Journal B

Integrable correlated electron model with next-nearest-neighbour interactions

Andrei A. Zvyagin, Andreas Klümper, J. Zittartz

Published Jan 1, 2001• 13 citations
Publisher
DOI
10.1007/s100510170347

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Advanced series in mathematical physics•May 1, 1994•0 citations
The authors study the droplet size distribution of the correlated site-bond percolation model introduced by Coniglio and Klein (1980), and also the usual clusters of two-dimensional Ising models near the critical point. Equilibrium configurations of the Ising model with nearest-neighbour interaction and also one with nearest- and next-nearest-neighbour interactions are generated through a Monte Carlo simulation, and then a cluster analysis is performed. The exponents beta and gamma for the Coniglio and Klein droplet distribution are found to agree, for both the nearest-neighbour and the next-nearest-neighbour model, with the corresponding exponents of the Ising model. The usual Ising clusters diverge only at T c in the Ising model with nearest-neighbour interaction but not for the model with next-nearest-neighbour interaction. The Potts model formulation is used to predict the behaviour of the droplet for general further-neighbour interactions.
Abstract An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The ground state and the elementary excitations are also studied. It is shown that the spinon excitation of the present model possesses a novel triple arched structure. The elementary excitation is gapless if the anisotropic parameter is real while the elementary excitation has an enhanced gap by the next-nearest-neighbour and chiral three-spin interactions if the anisotropic parameter is imaginary. The method of this paper provides a general way to construct integrable models with next-nearest-neighbour interactions.