  A few paradigmatic one-dimensional lattice-statistical spin models have
recently attracted a vigorous scientific interest owing to their peculiar
thermodynamic behavior, which is highly reminiscent of a temperature-driven
phase transition. The pseudotransitions of one-dimensional lattice-statistical
spin models differ from actual phase transitions in several important aspects:
the first-order derivatives of the Gibbs free energy such as entropy or
magnetization exhibit near a pseudo-transition an abrupt continuous change
instead of a true discontinuity, whereas the second-order derivatives of the
Gibbs free energy such as specific heat or susceptibility display near a
pseudo-transition a vigorous finite peak instead of an actual power-law
divergence. In the present chapter we will comprehensively examine a
pseudo-critical behavior of the spin-1/2 Ising diamond and tetrahedral chains
by a detailed examination of basic magnetothermodynamic quantities such as the
entropy, specific heat and susceptibility. It will be demonstrated that density
plots of these magnetothermodynamic quantities provide a useful tool for
establishing a finite-temperature diagram, which clearly delimits boundaries
between individual quasi-phases in spite of a lack of true spontaneous
long-range order at any nonzero temperature. It is suggested that a substantial
difference between the degeneracies of two ground states of the spin-1/2 Ising
diamond and tetrahedral chains is an essential prerequisite for observation of
a relevant pseudo-critical behavior in a close vicinity of their ground-state
phase boundary.
