  Recently gigantic peaks in thermodynamic response functions have been
observed at finite temperature for one-dimensional models with short-range
coupling, closely resembling a second-order phase transition. Thus, we will
analyze the finite temperature pseudo-transition property observed in some
one-dimensional models and its relationship with finite size effect. In
particular, we consider two chain models to study the finite size effects;
these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type
ladder model. Although the anomalous peaks of these one-dimensional models have
already been studied in the thermodynamic limit, here we will discuss the
finite size effects of the chain and why the peaks do not diverge in the
thermodynamic limit. So, we discuss the dependence of the finite size effects,
for moderately and sufficiently large systems, in which the specific heat and
magnetic susceptibility exhibit peculiar rounded towering peaks for a given
temperature. This behavior is quite similar to a continuous phase transition,
but there is no singularity. For moderately large systems, the peaks narrow and
increase in height as the number of unit cells is increased, and the location
of peak shifts slightly. Hence, one can naively induce that the sharp peak
should lead to a divergence in the thermodynamic limit. However, for a rather
large system, the height of a peak goes asymptotically to a finite value. Our
result confirms the dependence of the peak height with the number of unit cells
at the pseudo-critical temperature. We also provide an alternative empirical
function that satisfactorily fits specific heat and magnetic susceptibility at
pseudo-critical temperature. Certainly, our result is crucial to understand the
finite size correction behavior in quantum spin models, which in general are
only numerically tractable within the framework of the finite size analysis.
