@article{Johnston2001DecoratingRQ,
title={Decorating random quadrangulations},
author={Desmond A. Johnston and Ranasinghe P.K.C. Malmini},
journal={Journal of Physics A},
year={2001},
volume={35}
}

On various regular lattices (simple cubic, body centred cubic, etc) decorating an edge with an Ising spin coupled by bonds of strength L to the original vertex spins and competing with a direct anti-ferromagnetic bond of strength ?L can give rise to three transition temperatures for suitable ?. The system passes through ferromagnetic, paramagnetic, anti-ferromagnetic and paramagnetic phases respectively as the temperature is increased. For the square lattice on the other hand, multiple… Expand

A high‐temperature expansion of the partition function for a lattice of N spins with Hamiltonian H=−J ∑ (ij)σizσjz−mHz ∑ iσiz−mHx ∑ iσix is derived and thence an expansion for the zero‐field… Expand

We investigate the non-self-averaging properties of the dynamics of Ising, 4-state Potts and 10-state Potts models in single-cluster Monte Carlo simulations on quenched ensembles of planar, trivalent… Expand