Abstract
The renormalization-group method is applied to the analysis of phase transitions in systems where the order parameter is coupled to a nonordering additional variable . A variety of critical and tricritical behaviors or first-order transitions is found as a function of the physical variables and possible macroscopic constraints imposed on the system. For coupling, the correlation function of was found to be governed by a correlation length which is proportional to that of the order parameter, and by a critical index ; here is the specific-heat exponent of the appropriate unconstrained system. The singular part of the susceptibility, , has a critical exponent equal to , the true specific-heat exponent. When the coupling is , a weaker singularity of appears. The crossover between this behavior and the one typical to coupling is calculated. has a singular part with an exponent , in the unconstrained case. The breakdown of the scaling law related to the correlation function of in the constrained case is discussed.
- Received 9 April 1975
DOI:https://doi.org/10.1103/PhysRevB.12.2768
©1975 American Physical Society