Spin chain with a magnetic field and spinning string in a magnetic field background

We analyze the fast-moving string in the magnetic Melvin field background and find that the associated effective Lagrangian of string sigma model describes the spin-chain model with external magnetic field. The spin vector in the spin chain has been properly deformed and is living on the deformed two-sphere or deformed two-dimensional hyperboloid, depending on the direction around which the string is spinning. We describe in detail the characters of spin deformation and, in particular, see that this is a general property for a string moving in a class of deformed background.