  Ising's solution of a classical spin model famously demonstrated the absence
of a positive-temperature phase transition in one-dimensional equilibrium
systems with short-range interactions. No-go arguments established that the
energy cost to insert domain walls in such systems is outweighed by entropy
excess so that symmetry cannot be spontaneously broken. An archetypal way
around the no-go theorems is to augment interaction energy by increasing the
range of interaction. Here we introduce new ways around the no-go theorems by
investigating entropy depletion instead. We implement this for the Potts model
with invisible states.Because spins in such a state do not interact with their
surroundings, they contribute to the entropy but not the interaction energy of
the system. Reducing the number of invisible states to a negative value
decreases the entropy by an amount sufficient to induce a positive-temperature
classical phase transition. This approach is complementary to the long-range
interaction mechanism. Alternatively, subjecting positive numbers of invisible
states to imaginary or complex fields can trigger such a phase transition. We
also discuss potential physical realisability of such systems.
