A theory of critical phenomena in constrained systems

A general theory of critical phenomena in constrained systems is presented. An ideal second-order phase transition is assumed to occur in the unconstrained system. It is shown that this transition can either remain as it was, or be renormalized, or be changed into a first order transition when the system is constrained. Systems with an arbitrary number of constraints are discussed. Such systems have the advantage that the physical realizability of constraints which lead to a first order transition can be made more obvious. A soluble model is described which exemplifies all the different types of behaviour that are possible.