Role of nearest‐neighbour correlations in the site‐diluted spin‐1/2 Ising model

Baohua Teng, Yuanfu Chen, Hao Fu +4 more

Naeem Jan, Antonio Coniglio A, Dietrich Stauffer

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.

J. A. Plascak, J. Kamphorst Leal da Silva

Noureddine Benayad, A. Benyoussef, N. Boccara

2D spin-1 Ising models with nearest-neighbour and crystal-field interactions exhibit tricritical behaviour. A new method that applies to a wide class of random systems is used to study the influence of site and bond dilution on this behaviour. The authors have calculated temperature-crystal-field-concentration phase diagrams and determined, in particular, the influence of dilution on the zero-temperature critical field and on the tricritical temperature. The results are in agreement with those obtained recently for bond dilution by a real-space renormalisation-group technique. The method appears more tractable.

Anjan Kumar Chandra, Subinay Dasgupta

We consider the transverse Ising model in one dimension with nearest neighbour interaction and calculate exactly the longitudinal spin–spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of the one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use the Fisher–Hartwig conjecture. The result is that the correlation decays algebraically with distance ( n ) as 1/√ n and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.

M. Saber, J.W. Tucker