  In a previous paper [Weiguo Yin, Phys. Rev. Res. 6, 013331 (2024)], the
forbidden spontaneous phase transition in the one-dimensional Ising model was
found to be approachable arbitrarily closely in decorated ladders by
ultranarrow phase crossover (UNPC) at a given finite temperature $T_0$ with the
crossover width $2\delta T$ reduced exponentially, which resembles a genuine
first-order transition with large latent heat. Here, I reveal that the
forbidden phase transition can be approached at fixed $T_0$ as well in
decorated single-chain Ising models in the presence of a magnetic field, in
which $T_0$ is determined by the interactions involving only the decorated
parts and the magnetic field, while $2\delta T$ is independently, exponentially
reduced ($\delta T=0$ means a genuine transition) by restoring the
ferromagnetic interaction between the ordinary spins on the chain backbone --
which was neglected in the previous studies of pseudotransition -- thus
manifesting that this asymptoticity to the forbidden transition is essentially
the buildup of coherence in preformed crossover of local states. Furthermore, I
show that the UNPC can be realized even in the absence of the conventional
geometric frustration because the magnetic field itself can induce previously
unnoticed hidden spin frustration. These findings make the doors wide open to
the engineering and utilization of UNPC as a new paradigm for exploring exotic
phenomena and 1D device applications.
