RESUMEN
Recently, a kind of finite-temperature pseudotransition was observed in several quasi-one-dimensional models. In this work, we consider a genuine one-dimensional extended Hubbard model in the atomic limit, influenced by an external magnetic field and with the arbitrary number of particles controlled by the chemical potential. The one-dimensional extended Hubbard model in the atomic limit was initially studied in the seventies and has been investigated over the past decades, but it still surprises us today with its fascinating properties. We rigorously analyze its low-temperature behavior using the transfer matrix technique and provide accurate numerical results. Our analysis confirms that there is an anomalous behavior in the half-filled band, specifically occurring between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. Previous investigations did not deeply identify this anomalous behavior, maybe due to the numerical simplicity of the model, but from an analytical point of view this is not so easy to manipulate algebraically because one needs to solve an algebraic cubic equation. In this study, we explore this behavior and clearly distinguish the pseudotransition, which could easily be mistaken with a real phase transition. This anomalous behavior mimics features of both first- and second-order phase transitions. However, due to its nature, we cannot expect a finite-temperature phase transition in this model.
RESUMEN
Recently, it has been rigorously verified that several one-dimensional (1D) spin models may exhibit a peculiar pseudo-transition accompanied with anomalous response of thermodynamic quantities in a close vicinity of pseudo-critical temperature. In the present work we will introduce and exactly solve a mixed spin-(1/2,1) Ising-Heisenberg double-tetrahedral chain in an external magnetic field as another particular example of 1D lattice-statistical model with short-range interactions that displays a pseudo-transition of this type. The investigated model exhibits at zero temperature three ferrimagnetic phases, three frustrated phases, and one saturated paramagnetic phase. The ground-state phase diagram involves five unusual interfaces (phase boundaries), at which the residual entropy per site equals to a larger entropy of one of two coexisting phases. Four such interfaces are between a non-degenerate ferrimagnetic phase and a macroscopically degenerate frustrated phase, while one interface is between two non-degenerate ferrimagnetic phases. Though thermal excitations typically destroy all fingerprints of zero-temperature phase transitions of 1D lattice-statistical models with short-range forces, the mixed spin-(1/2,1) Ising-Heisenberg double-tetrahedral chain is quite robust with respect to thermal excitations and it displays peculiar pseudo-transitions close to all five aforementioned interfaces.