  Recently pseudo-critical temperature clues were observed in one-dimensional
spin models, such as the Ising-Heisenberg spin models, among others. Here we
report a relationship between the zero-temperature phase boundary residual
entropy (critical residual entropy) and pseudo-transition. Usually, the
residual entropy increases in the phase boundary, which means the system
becomes more degenerate at the phase boundary compared to its adjacent states.
However, this is not always the case; at zero temperature, there are some phase
boundaries where the entropy holds the largest residual entropy of the adjacent
states. Therefore, we can propose the following conjecture: If residual entropy
at zero-temperature is a continuous function at least from the one-sided limit
at a critical point, then pseudo-transition evidence will appear at finite
temperature near the critical point. We expect that this argument would apply
to study more realistic models. Only by analyzing the residual entropy at zero
temperature, one could identify a priori whether the system will exhibit the
pseudo-transition at finite temperature. To strengthen our conjecture, we use
two examples of Ising-Heisenberg models, which exhibit pseudo-transition
behavior: one frustrated coupled tetrahedral chain and another unfrustrated
diamond chain.
