Modulated Structures in the Annni Model With an External Magnetic Field Near Criticality

Abstract

Conditions for a phase transition from the paramagnetic state to the modulated structure are found in a class of anisotropic Ising models with an external magnetic field. The critical value of the external magnetic field is obtained. Branching equations are derived and small branching theorems are proven for commensurate and incommensurate configurations. Here we consider a class of anisotropic Ising models with an external magnetic field and show a phase transition from the paramagnetic state to spatially inhomogeneous commensurate configuration or incommensurate one below the critical magnetic field. To be more exact, we illustrate the method on the ANNNI model [1,2], but one can apply it to models with an arbitrary number of interacting neighbours.Any N 1 -periodic configuration x can be expressed [3] aswhere