  For several decades now it has been known that systems with shearless
invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic
transport. These barriers are resilient to breakage under perturbation and
therefore regions where they occur are natural places to look for barriers to
transport. We describe a novel kind of effective barrier that persists after
the shearless torus is broken. Because phenomena are generic, for convenience
we study the Standard Nontwist Map (SNM), an area-preserving map that violates
the twist condition locally in the phase space. The novel barrier occurs in
nontwist systems when twin even period islands are present, which happens for a
broad range of parameter values in the SNM. With a phase space composed of
regular and irregular orbits, the movement of chaotic trajectories is hampered
by the existence of both shearless curves, total barriers, and a network of
partial barriers formed by the stable and unstable manifolds of the hyperbolic
points. Being a degenerate system, the SNM has twin islands and, consequently,
twin hyperbolic points. We show that the structures formed by the manifolds
intrinsically depend on period parity of the twin islands. For this even
scenario the novel structure, named a torus free barrier, occurs because the
manifolds of different hyperbolic points form an intricate chain atop a dipole
configuration and the transport of chaotic trajectories through the chain
becomes a rare event. This structure impacts the emergence of transport, the
escape basin for chaotic trajectories, the transport mechanism and the chaotic
saddle. The case of odd periodic orbits is different: we find for this case the
emergence of transport immediately after the breakup of the last invariant
curve, and this leads to a scenario of higher transport, with intricate escape
basin boundary and a chaotic saddle with non-uniformly distributed points.
