"Magnon" is a boson which takes a role of magnetic excitations in magnetic materials. "Plateau" of magnetization under the magnetic fields can be understood as the localization of magnons with a certain pattern in the real space. In spite of this simple picture, it is difficult to calculate the energy of the magnon as functions of the concentration and temperatures etc. due to the many-body nature of the system.

We succeeded in calculating the essentially exact energy of magnons near the saturated field in frustrated magnet, especially spin S=1/2 system on Kagome lattice. To do this, we mapped the Hamiltonian into that of Ising model on the dual lattice. We could calculate the low temperature energy of this mapped model exactly. From this, we proved that there is a finite temperature phase transition which breaks translational symmetry in Kagome lattice and this corresponds to the 9/7 plateau. We find that the universality class of this transition belongs to that of three states Pott's model.