  The study of frustrated spin systems often requires time-consuming numerical
simulations. As the simplest approach, the classical Ising model is often used
to investigate the thermodynamic behavior of such systems. Exploiting the small
correlation lengths in frustrated Ising systems, we develop a method for
obtaining a first approximation to the energetic properties of frustrated
two-dimensional Ising systems using small networks of less than 30 spins. These
small networks allow much faster numerical simulations, and more importantly,
analytical calculation of the properties from the partition function is
possible. We choose Ising systems on the triangular lattice, the Kagome
lattice, and the triangular Kagome lattice as prototype systems and find small
systems that can serve as good approximations to these prototype systems. We
also develop criteria for constructing small networks to approximate general
two-dimensional frustrated Ising systems. This method of using small networks
provides a novel and efficient way to obtain a first approximation to the
properties of frustrated spin systems.
