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 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.
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.
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.
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.
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice exhibits an intriguing temperature-driven phase transition in a magnetic field between a classical ferrimagnetic phase and a quantum monomer-dimer phase. A generalized decoration-iteration transformation accurately maps the considered model to an effective spin-1/2 Ising model on a square lattice with temperature-dependent effective interactions and field, whereby the effective field vanishes at the phase boundary separating the classical ferrimagnetic phase from the quantum monomer-dimer phase. Typical features of the magnetization, magnetic susceptibility and specific heat in the vicinity of discontinuous and continuous thermal phase transitions between the classical ferrimagnetic phase and the quantum monomer-dimer phase are elucidated.
The low-dimensional quantum spin systems have been extensively studied in the past three decades due to the novel ground states and rich magnetic behaviors,especially the quantum spin chain with diamond topology structure. Motivated by recent experimental success in Cu3(CO3)2(OH)2 compound,which is regarded as a model material of spin-1/2 diamond chain,researchers have paid a lot of attention to various variants of diamond spin chains.In this paper,we mainly examine the magnetic properties of an antisymmetric spin-1/2 Ising-Heisenberg diamond chain with the secondneighbor interaction between nodal spins.By using exact diagonalization and transfer-matrix methods,the ground-state phase diagram,magnetization behavior and macroscopic thermodynamics are exactly solved for the particular case that all magnetic bonds yield antiferromagnetic couplings,which usually shows the most interesting magnetic features closely related to a striking interplay between geometric frustration and quantum fluctuations.To clearly illustrate the effect of second-neighbor interaction item,we consider a highly frustrated situation that all Ising-Heisenberg bonds and Heisenberg bonds possess the same interaction strength.The calculation results indicate that the second-neighbor interaction item will enrich ground states and magnetization plateaus.A classical ferrimagnetic phase FRI1 corresponding to a novel two-thirds of intermediate plateau with translationally broken symmetry is introduced,manifesting itself as up-up-up-down-up-up spin configuration at a ground-state.In addition,there are other four distinct ground states which can be identified from the phase diagram,i.e.,one saturated paramagnetic phase SP,one classical ferrimagnetic phase FRI2,one quantum ferrimagnetic phase QFI and the unique quantum antiferromagnetic phase QAF.The classical phase FRI2 and quantum phase QFI both generate one-third of magnetization plateau.It is worth mentioning that all the values of these magnetization plateaus satisfy the Oshikawa-Yamanaka-Affleck condition.Besides,the results also have shown a rich variety of temperature dependence of total magnetization and specific heat.The magnetization displays the remarkable thermal-induced changes as the external field is sufficiently close to critical value where two or more than two different ground states coexist.At the critical field relevant to a coexistence of two different states,the total magnetization displays a monotonic decrease trend.The thermal dependence of zero-field specific heat displays relative complex variations for different second-neighbor interactions between nodal spins.At first,the specific heat presents only a single rounded Schottky-type maximum.Using the second-neighbor interaction,another sharp peak arises at low-temperature and is superimposed on this round maximum,and the specific heat exhibits a double-peak structure. On further strengthening,the low-temperature one keeps its height shifting towards high temperature,while the hightemperature round peak suffers great enhancement and moves in an opposite direction.Finally,the low temperature peak entirely merges with the Schottky-type peak at a certain value of second-neighbor interaction,and above this value, the specific curve recovers its single peak structure.The observed double-peak specific heat curves mainly originate from thermal excitations between the ground-state spin configuration QAF and the ones close enough in energy to the ground state.
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.