Simulating Computationally Complex Magnetic Molecules

The following sections are included: • Introduction o Scope and purpose o Introduction to the Heisenberg Hamiltonian o Usefulness and limitations of matrices • Quantum Monte Carlo Simulations o Avoiding the ‘roadblock’ of large matrices o Energy spectrum for symmetric rings o Applications to heterometallic rings o Applications to frustrated magnetic molecules • Classical Spin Dynamics Simulations o The classical Heisenberg Hamiltonian o Classical Monte Carlo simulations  The spin equations of motion o Heat bath simulational methods o Revealing novel physics in magnetic molecules with classical methods  Competing spin phases and exchange disorder in the Keplerate type molecules {Mo72Fe30} and {Mo72Cr30}  Metamagnetic phase transitions in magnetic polytopes  Critical slowing-down in Heisenberg magnetic molecules