  There are some particular one-dimensional models, such as the
Ising-Heisenberg spin models with a variety of chain structures, which exhibit
unexpected behaviors quite similar to the first and second order phase
transition, which could be confused naively with an authentic phase transition.
Through the analysis of the first derivative of free energy, such as entropy,
magnetization, and internal energy, a "sudden" jump that closely resembles a
first-order phase transition at finite temperature occurs. However, by
analyzing the second derivative of free energy, such as specific heat and
magnetic susceptibility at finite temperature, it behaves quite similarly to a
second-order phase transition exhibiting an astonishingly sharp and fine peak.
The correlation length also confirms the evidence of this pseudo-transition
temperature, where a sharp peak occurs at the pseudo-critical temperature. We
also present the necessary conditions for the emergence of these quasi-phases
and pseudo-transitions.
