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), whereas 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 parts of the peak with power-law "pseudo-critical" exponents. We determine the pseudo-critical exponents in the temperature range where these peaks are developed, namely, ν=1 for the correlation length and α=3 for the specific heat. We also study the behavior of the electron density and isothermal compressibility around the pseudo-critical temperature.
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), whereas 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 parts of the peak with power-law "pseudo-critical" exponents. We determine the pseudo-critical exponents in the temperature range where these peaks are developed, namely, ν=1 for the correlation length and α=3 for the specific heat. We also study the behavior of the electron density and isothermal compressibility around the pseudo-critical temperature.
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.
The spin-1/2 Ising diamond chain in a magnetic field displays a remarkable pseudo-transition whenever it is driven sufficiently close to a ground-state phase boundary between a classical ferrimagnetic phase and a highly degenerate frustrated phase.The pseudo-transition of the spin-1/2 Ising diamond chain relates to intense thermal excitations from a nondegenerate ferrimagnetic ground state to a highly degenerate manifold of excited states with a frustrated character, which are responsible for an anomalous behavior of thermodynamic quantities.Temperature dependences of entropy and specific heat are indeed reminiscent of a temperature-driven phase transition of a discontinuous (entropy) or continuous (specific heat) nature though there are no true singularities of these thermodynamic quantities at a pseudo-critical temperature.
The q-state Potts model on a diamond chain has mathematical significance in analyzing phase transitions and critical behaviors in diverse fields, including statistical physics, condensed matter physics, and materials science. By focusing on the three-state Potts model on a diamond chain, we reveal rich and analytically solvable behaviors without phase transitions at finite temperatures. Upon investigating thermodynamic properties such as internal energy, entropy, specific heat, and correlation length, we observe sharp changes near zero temperature. Magnetic properties, including magnetization and magnetic susceptibility, display distinct behaviors that provide insights into spin configurations in different phases. However, the Potts model lacks genuine phase transitions at finite temperatures, in line with the Peierls argument for one-dimensional systems. Nonetheless, in the general case of an arbitrary q state, magnetic properties such as correlation length, magnetization, and magnetic susceptibility exhibit intriguing remnants of a zero-temperature phase transition at finite temperatures. Furthermore, residual entropy uncovers unusual frustrated regions at zero-temperature phase transitions. This feature leads to the peculiar thermodynamic properties of phase boundaries, including a sharp entropy change resembling a first-order discontinuity without an entropy jump, and pronounced peaks in second-order derivatives of free energy, suggestive of a second-order phase transition divergence but without singularities. This unusual behavior is also observed in the correlation length at the pseudocritical temperature, which could potentially be misleading as a divergence.
We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.
Quasicritical exponents of one-dimensional models displaying a quasitransition at finite temperatures are examined in detail. The quasitransition is characterized by intense sharp peaks in physical quantities such as specific heat and magnetic susceptibility, which are reminiscent of divergences accompanying a continuous (second-order) phase transition. The question whether these robust finite peaks follow some power law around the quasicritical temperature is addressed. Although there is no actual divergence of these quantities at a quasicritical temperature, a power-law behavior fits precisely both ascending as well as descending parts of the peaks in the vicinity but not too close to a quasicritical temperature. The specific values of the quasicritical exponents are rigorously calculated for a class of one-dimensional models (e.g., Ising-XYZ diamond chain, coupled spin-electron double-tetrahedral chain, Ising-XXZ two-leg ladder, and Ising-XXZ three-leg tube), whereas the same set of quasicritical exponents implies a certain "universality" of quasitransitions of one-dimensional models. Specifically, the values of the quasicritical exponents for one-dimensional models are: α=α^{'}=3 for the specific heat, γ=γ^{'}=3 for the susceptibility and ν=ν^{'}=1 for the correlation length.
We consider the finite-temperature properties of the extended Bose-Hubbard model realized recently in an ETH experiment [Nature 532, 476 (2016)]. Competing short- and global-range interactions accommodate fascinating collective phenomena. We formulate a self-consistent mean-field theory to describe the behaviors of the system at finite temperatures. At a fixed chemical potential, we map out the distributions of the superfluid order parameters and number densities with respect to the temperatures. For a charge density wave, we find that the global-range interaction enhances the charge order by increasing the transition temperature at which the charge order melts out, while for a supersolid phase, we find that the disappearance of the charge order and the superfluid order occurs at different temperature. At a fixed number-density filling factor, we extract the temperature dependence of the thermodynamic functions such as internal energy, specific heat and entropy. Across the superfluid phase transition, the specific heat has a discontinuous jump.