Phase diagram of the polyhedral spin models on square lattice with diluted bonds

The study of phase transition is an important subject in condensed matter physics as some materials are more versatile when they are at certain phase. The low temperature ferromagnetic phase of magnetic material is a rm example of these. Passing by the Curie temperature, the paramagnetic phase of magnetic materials will change to a ferromagnetic phase. There are three main variables controlling a magnetic phase transition, namely the symmetry of spins, coupling interaction and the lattice structure. It is known that the discreteness can create low temper ature magnetic order, exempli ed by the existence of a true- long range order for the 2D 6-state clock model at lower temperature [1, 2] In this talk we present our study of the ferromagnetic polyhedral spins model on square lattice with bond dilution. Polyhedral spins are the discrete counterpart of the continuous Heisenberg spin model. Two polyhedral spin models, i.e., the icosahedoron and dodecahedron model are discussed. As previously reported, the non-diluted (pure) ferromagnetic case of these models exhibits nite temperature phase transition [3]. We use Monte Carlo simulation with a newly introduced algorithm, two-size PCC algorithm [4]; and probe whether the existing phase transitions are signi cantly a ected by the bond dilution. We simulate the models with various bond concentrations and calculate their corresponding critical temperatures. The phase diagram of the models are presented as a plot of the obtained critical temperatures with respect to their corresponding bond concentrations