Since Ernst Ising's proof one century ago, it has been well-known that phase transition at finite temperature does not exist in the Ising model with short-range interactions in one dimension. Yet, little is known about whether this forbidden transition could be approached arbitrarily closely -- at fixed finite temperature. To explore such asymptoticity, the notion of marginal phase transition (MPT) was introduced recently and spontaneous MPT was successfully found in decorated ladder Ising models. On the other hand, in the presence of a magnetic field, narrow phase crossover termed as pseudo-transition was found in decorated single-chain Ising models with strong geometric frustration; it is thus imperative to know whether the pseudo-transition could be transformed to approach a genuine transition at fixed finite temperature $T_0$ arbitrarily closely, i.e., being the MPT. Here, I reveal the existence of the field-induced MPT in decorated Ising chains, in which $T_0$ is determined by the interactions involving only the decorated parts and the magnetic field, while the crossover width $2\delta T$ is independently, exponentially reduced ($\delta T = 0$ means a genuine transition) by the previously neglected ferromagnetic interaction between the ordinary spins on the chain backbone. Furthermore, I show that the MPT can be realized even in the decorated Ising chains without geometric frustration because the magnetic field itself can induce previously unnoticed hidden spin frustration. These findings manifest that MPT is essentially the buildup of coherence in preformed crossover of any local states, making the doors wide open to the engineering and utilization of MPT as a new paradigm for exploring exotic phenomena and 1D device applications.
Comment: 19 pages, 7 figures