The simple quadratic Ising model with crossing bonds

We investigate the ferromagnetic critical line of the simple quadratic Ising model with nearest-neighbour and next-nearest-neighbour interactions, by means of Monte Carlo, renormalisation group and analytic methods. A comparison of the Monte Carlo results with the renormalisation group trajectories yields the asymptotic behaviour of the critical line in the strong-coupling limit. A number of figures of spin configurations is included to illustrate the physical behaviour of the model.