# Defectively crossovers between two-dimensional two-state fields in the presence of an external magnetic field

Comments: 5 pages, revtex4; minor changes and references added

We study the two-dimensional two-state field in the presence of an external magnetic field. We study the defect-free two-state solutions of the QFT theory for one-component fields in the two-dimensional field theory. The defect-free solutions have three-dimensional areas, and we find that there is a first-order differential equation which is a consequence of the absence of any external magnetic field. We then compute the first-order equations for the defect-free solution for the two-dimensional two-state field in the presence of an external magnetic field, and find that their dimension is very small.