We consider the long wave approximation of the Ising model which corresponds to the ϕ4 field theory with a scalar field ϕ. This model is used as a paradigm of a system with a continuous phase transition. Fluctuations are gaining importance with the decrease of the spatial dimension. The dimension at which the transition disappears is called the lower critical dimension. The lower critical dimension for the present system is dl = 1, where the exact solution is known. Still, here we attempt to apply the methods of the nonperturbative renormalisation group (NPRG) to obtain an approximative solution. The ultimate goal is to, in future, develop a novel approach to handling critical statistical systems in the lower critical dimension via NPRG that could be extended to systems without exact solutions. Using certain nonperturbative approximation schemes, we find a description of the system in the vicinity and at the lower critical dimension. We find the lower critical dimension to be in good agreement with the exact dl = 1. A new result that we find is that the effective potential U shows nonanalyticity at a finite field, but in a way that is consistent with the expected physical behavior of the system.