  Through the direct decoration transformation approach, we obtain a general
solution for the pentagonal Ising model, showing its equivalence to the
isotropic free-fermion eight-vertex model. We study the ground-state phase
diagram, in which one ferromagnetic (FM) state, one ferrimagnetic (FIM) state,
and one frustrated state are found. Using the exact solution of the pentagonal
Ising model, we discuss the finite-temperature phase diagrams and find a phase
transition between the FIM state and the disordered state as well as a phase
transition between the disordered state and the FM state. We also discuss some
additional remarkable properties of the model, such as the magnetization,
entropy, and specific heat, at finite temperature and at its low-temperature
asymptotic limit. Because of the influence of the second-order phase transition
between the frustrated and ferromagnetic phases, we obtain surprisingly low
values of the entropy and the specific heat until the critical temperature is
reached.

Statistical Mechanics