Competing interactions in magnetic systems: studies on some low dimensional spin models.

The study of the effects of competing interactions, more commonly called  "frustration", is one of the important themes in research on magnetic systems.  In this talk I will present some aspects of this diverse subject using my work  on a selection of lattice models. I will begin with a study of the ground state phase diagram of a frustrated mixed-spin ladder with spin-1/2 and spin-1 rungs alternating with each other.  Frustration induces phase transitions between four different ground states : two paramagnetic and two different partially magnetised phases.   In a closely related model with all spins the same, I will demonstrate the existence of (exactly solvable) magnetisation plateaus connected by jumps which appear through an interplay of frustration and a magnetic  field. Finally, I will discuss our ongoing efforts to study the spin-1/2  nearest neighbour antiferromagnet on the Kagome lattice using Contractor  Renormalisation (CORE). I will outline the technical challenges involved in using a large (12 site) building block and present a method to compute  the spectra of reasonably large system sizes (up to 36 spin-1/2 sites)  with modest computational resources.