Tricriticality and persistency of trails and silhouettes

Trails and silhouettes (polymers with loops) are generated using exact enumeration on a face-centred cubic lattice. By assigning a tunable fugacity factor with each intersection it is observed that, as the fugacity for intersections is increased the trail and silhouette configurations change from swollen to compact ones, indicating the existence of tricritical points. Strong divergence of the specific heats for different path lengths is used to locate these tricritical points. The Dlog Pade scheme is used to compute the corresponding tricritical exponents in the limit of large path lengths. The tricritical exponents thus obtained show that these tricritical points are distinct from the usual Theta point, and that trails and silhouettes do not belong to the SAW universality class. The tricritical exponents further show that trails and silhouettes do not belong to the same universality class. Persistency arising from fixing the initial step is also investigated and it is found that odd moments of the persistency obey a power law that can be expressed in terms of the critical exponent, nu , and the path length l.