The 2D Blume Capel model : fermionisation and phase diagram
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
The Blume-Capel model was introduced as an extension of the Ising model, to mimic the physical properties of the liquid mixture of Helium 3 and 4 at low temperature. Mean field theory and Monte Carlo studies show that the phase diagram exhibits a line of second order critical points ending at a tricritical point in the phase diagram. We use a Grassmann algebra technique developed by V. Plechko to derive the exact underlying fermionic field theory for the 2D Blume-Capel. The analysis of this action allows us to characterize the exact critical line.