ϕ⁴ model under Dirichlet-Neumann boundary conditions

Abstract The minimization of the Ginsburg-Landau ϕ 4 functional is at core of the so-called ϕ 4 model, which is one of the basic models of statistical mechanics. The minimization leads to a second order nonlinear differential equation that has to be solved under specific boundary conditions. In the current article we consider a system with a film geometry with thickness L under Dirichlet-Neumann boundary conditions applied along the finite-direction. We study the modifications of the bulk phase diagram for the finite system, as well as the field-temperature behavior of the characterizing the system order parameter profile, as well as the connected to it corresponding response functions (local and total susceptibilities).