Static Field Instantons Of 2+1 Dimension And Domain Structures In Magnetic Film

It is our main purpose to extend the static instantons of scalar 4 - andsine-Gordon-theory of 1+1 dimension to that of 2+1 dimension . First, we give a brief review of instanton theory of 1+1 dimension .Then we obtain the instantons in 4 -field model of 2+1 dimension . In the last part of the paper, we derive theEuclidean equation of motion of the magnetic vector in a theoretical magnetic film consisting of biaxial-anisotropic molecular ferromagnets ,which is reduced to the 2+1 dimensional sine-Gordon field equation in the strong anisotropy limit .We obtain various domain structures which are the static solutions of the sine-Gordon field equation. In particular, it is found that static instantons are just domain wall solutions in the magnetic film. Stability of the domain walls is also investigated in terms of the instanton theory.