Abstract

Many condensed matter problems, such as ordering of a classical ferromagnet or fluid-fluid phase separation, are described by dynamical field theories in which a scalar field obeys a noisy gradient flow governed by a quartic effective potential. These theories are called Model A and Model B for the cases of a non-conserved and conserved scalar, respectively. Traditionally, such models are constructed to obey detailed balance, so that the system evolves to the Boltzmann distribution, giving time-reversible fluctuations at stationarity. Reaching the equilibrium state can be nontrivial however: starting from a metastable uniform initial condition, it requires an instanton to nucleates a droplet large enough to then grow spontaneously. In recent years, attention has shifted to systems without detailed balance, whose stationary states are non-Boltzmann and involve continuous entropy production with time-asymmetric fluctuations. (One example is the study of phase separation among self-propelled particles such as swimming bacteria.) To describe such cases, we have recently introduced variants of Models A and B that break detailed balance explicitly. I will outline some of the qualitative and quantitative novelties that arise in the critical phenomena, steady states, and instantons of these new theories.