Effect of Magnetic Field on Electronic Nematic Order in a Bilayer System: Application to Sr$_{3}$Ru$_{2}$O$_{7}$

Recent experiments on the bilayer compound Sr$_{3}$Ru$_{2}$O$_{7}$ suggest the existence of an electronic liquid-crystal phase. A possible explanation for the unusual behavior observed in this material is provided by an electronic nematic theory. Within this framework, a bilayer system undergoes multiple phase transitions and exhibits strong transport anisotropy. The model also incorporates an external in-plane magnetic field to study the effect on metamagnetic transitions and anisotropic transport. Details of our numerical calculations will be presented.