The statistical steady state of the noisy dynamics of lasers with an absorptive nonlinearity is mapped to equilibrium fluctuations of a scalar field with an unstable self-interaction and a global power constraint. The free energy is calculated using mean field arguments, which are shown to be exact in the thermodymic limit. The outcome is a simple but nontrivial phase diagram of passive mode locking, which resolves the long standing issue of the "second" threshold of passive mode locking in lasers.