Conformal field theories describe the behaviour of critical systems, and logarithmic modells are relevant for disordered systems, or percolation. The simplest logarithmic conformal field theory is the symplectic fermion model. To be able to study the model in concrete way, it is necessary to have a practical construction for the Hilbert space and the operators. This forms the primary aim of the proposed project, from which one can progress to study the vicinity of the critical point and the behaviour of renormalisation group flows. This work is also an opportunity for the student to deepend their knowledge of quantum field theory, to familiarise themselves with conformal field theory and statistical field theory, and to learn the fundamental calculational methods in practice as well.