Relaxing the geodesic rule in defect formation algorithms

In studying the formation of topological defects, it is conventional to assume the “geodesic rule” which is equivalent to minimizing gradients of the order parameter. This assumption has been called into question in field-theoretic studies of first order phase transitions and in the case of local defects. We present a scheme for numerically investigating the formation of strings without assuming the geodesic rule. Our results show that the fraction of string in infinite strings grows as we deviate from the geodesic rule.