Quantum field theory models with a large number of colors and the statistical physics of disordered systems

An analogy is noted between $N\times N$ matrix models of quantum field theory in the limit $N\to\infty$ and models of disordered spin systems in statistical physics. The replica method is used to establish the existence in the large $N$ limit for the matrix model $\varphi_D^4$ of a new phase analogous to the spin glass phase in disordered spin systems.