In this talk, I will introduce a generalisation of the Ising model called the $\varphi^4$ model, which was originally introduced in quantum field theory as the simplest candidate for a non-Gaussian theory. Its importance in statistical physics was highlighted by Griffiths and Simon, who observed that the $\varphi^4$ potential arises as the scaling limit of the fluctuations of the critical Ising model on the complete graph. I will describe how this connection to the Ising model leads to two new geometric representations of the $\varphi^4$ model, called the random tangled current expansion and the random cluster model. I will then explain how these representations can be used to prove that the phase transition of the $\varphi^4$ model is continuous in dimensions three and higher, and to obtain large-deviation estimates for spin averages in the supercritical regime. Based on joint works with Trishen Gunaratnam, Romain Panis and Franco Severo.