In preimplantation mammalian embryos, the second cell fate decision introduces spatial patterns of embryonic and extra-embryonic precursor cells. The transcription factors NANOG and GATA6 are the earliest markers for the two cell types and interact between cells via the fibroblast growth factor signaling pathway. Computational models have been used to mimic the patterns and cell type proportions found in experimental studies. However, these models are always phenomenological in nature and lack a proper physical explanation. We derive a cell fate decision model motivated by the ideas of statistical mechanics. The model incorporates intra- and intercellular interactions of NANOG and GATA6. A detailed mathematical analysis on the resulting dynamical system is presented. We find that our model is capable of generating tissue wide spatial patterns of the two cell types. Its advantages are revealed in the simple physical and biological interpretation of the parameters and their interactions. In numerical simulations, we showcase the ability to replicate checkerboard patterns of different cell type proportions varying only a single parameter. The tight control of the system as well as the ease of use and the direct expandability to other signaling types provide solid reasons for the continued use of our model. We are convinced that our approach presents an exciting perspective in relation to cell fate decisions. Moreover, the concepts are generalizable to questions regarding cell signaling beyond the mammalian embryo.