ISING CRITICALITY: FROM QUANTUM MAGNETISM TO MAJORANA QBITS
The Ising model is a paradigmatic example of phase transitions and critical phenomena, and is still of central importance in modern low dimensional quantum systems. Importantly this model formulated originally in terms of spins, has an equivalent fermionic description. This allows for a unifying formulation of very different electron systems, ranging from quantum wires supporting Majorana edge stats to quantum dots in the two channel Kondo geometry, in terms of analogous magnetic systems. For example, the two channel Kondo model presents an intriguing and theoretically difficult problem due to its electronic non-Fermi liquid behavior. Moreover this critical point is extremely unstable against symmetry breaking perturbations which make experiments very demanding. Here I show how the physics of this instability is directly connected with models of Ising spins. This way, new universal predictions for quantum dot experiments capturing the entire crossover from non-Fermi liquid to Fermi liquid will be presented and discussed.