  Here we consider a one-dimensional $q$-state Potts model with an external
magnetic field and an anisotropic interaction that selects neighboring sites
that are in the spin state 1. The present model exhibits an unusual behavior in
the low-temperature region, where we observe an anomalous vigorous change in
the entropy for a given temperature. There is a steep behavior at a given
temperature in entropy as a function of temperature, quite similar to
first-order discontinuity, but there is no jump in the entropy. Similarly,
second derivative quantities like specific heat and magnetic susceptibility
also exhibit a strong acute peak rather similar to second-order phase
transition divergence, but once again there is no singularity at this point.
Correlation length also confirms this anomalous behavior at the same given
temperature, showing a strong and sharp peak which easily one may confuse with
a divergence. The temperature where occurs this anomalous feature we call
pseudo-critical temperature. We have analyzed physical quantities, like
correlation length, entropy, magnetization, specific heat, magnetic
susceptibility, and distant pair correlation functions. Furthermore, we analyze
the pseudo-critical exponent that satisfy a class of universality previously
identified in the literature for other one-dimensional models, these
pseudo-critical exponents are: for correlation length $\nu=1$, specific heat
$\alpha=3$ and magnetic susceptibility $\mu=3$.
