We discuss some interesting classical and quantum phase transitions. The classical 2d spin 1 Blume-Capel model is a non-integrable model, but it exhibits a tricritical point described by a CFT which can be located only numerically. We show how we can determine this point using the concepts of Entanglement entropy, employing classical Monte Carlo simulations coupled with the knowledge that the critical theory is a minimal model with c=0.7.
In the next part, we discuss how to formulate QFT for certain Non-Fermi liquid systems. We also demonstrate that the superconducting instability in such systems is enhanced by order parameter fluctuations.