Singularities near critical and bicritical end points: applications to an isomorphous transition

We study a system that has an isomorphous transition using an eighth-order Landau-type free energy function. The phase diagram of such system has a critical line that meets a first-order phase boundary at a critical end point. This phase boundary is also limited by two other critical lines that meet at a bicritical end point. We showed that this phase boundary close to the end point exhibits a nonanalytic behavior associated with the singularities of the critical line, confirming similar result we previously obtained using scaling arguments. Related universal amplitude ratios are then computed. Next, the critical lines near the bicritical end point are also analyzed and checked for singularities.