  One-dimensional systems with short-range interactions cannot exhibit a
long-range order at nonzero temperature. However, there are some particular
one-dimensional models, such as the Ising-Heisenberg spin models with a variety
of lattice geometries, which exhibit unexpected behavior similar to the
discontinuous or continuous temperature-driven phase transition. Although these
pseudo-transitions are not true temperature-driven transitions showing only
abrupt changes or sharp peaks in thermodynamic quantities, they may be confused
while interpreting experimental data. Here we consider the spin-$\frac{1}{2}$
Ising-XYZ diamond chain in the regime when the model exhibits
temperature-driven pseudo-transitions. We provide a detailed investigation of
several correlation functions between distant spins that illustrates the
properties of quasi-phases separated by pseudo-transitions. Inevitably, all
correlation functions show the evidence of pseudo-transition, which are
supported by the analytical solutions and, besides we provide a rigorous
analytical investigation around the pseudo-critical temperature. It is worth to
mention that the correlation functions between distant spins have an extremely
large correlation length at pseudo-critical temperature.
