  We consider the extended Hubbard diamond chain with an arbitrary number of
particles driven by chemical potential. The interaction between dimer diamond
chain and nodal couplings is considered in the atomic limit (no hopping), while
the dimer interaction includes the hopping term. We demonstrate that this model
exhibits a pseudo-transition effect in the low-temperature regime. Here, we
explore the pseudo-transition rigorously by analyzing several physical
quantities. The internal energy and entropy depict sudden, although continuous,
jumps which closely resembles discontinuous or first-order phase transition. At
the same time, the correlation length and specific heat exhibit astonishing
strong sharp peaks, quite similar to a second-order phase transition. We
associate the ascending and descending part of the peak with power-law
\textquotedbl pseudo-critical\textquotedbl exponents. We determine the
pseudo-critical exponents in the temperature range where these peaks are
developed, namely $\nu=1$ for the correlation length and $\alpha=3$ for the
specific heat. We also study the behavior of the electron density and
isothermal compressibility around the pseudo-critical temperature.
