We investigate in detail the influence of the violation of the strict residual-entropy hierarchy among the neighboring ground states of different orders on the low-temperature behavior of the specific heat capacity in the magnetic frustrated systems in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model with the multisite interaction in the presence of the external magnetic field on the zigzag ladder. The exact expressions for the residual entropies of all ground states of the model are found, and it is shown that when the strength of the multisite interaction is strong enough then the model exhibits a quite interesting specific situation, namely, that there exist neighboring plateau ground states together with the single-point ground state that separates them, such that the magnetization properties of all of them are different but their entropy per site is the same and equal to zero. It is shown that this fact of the violation of the strict residual-entropy hierarchy between neighboring ground states of different orders leads to the reduction of the possible number of peaks that can appear in the low-temperature behavior of the specific heat capacity in the corresponding regions of the model parametric space. In addition, it is also shown that the absence of the strict residual-entropy hierarchy among neighboring ground states of different orders changes qualitatively the behavior of the specific heat capacity as a function of the external magnetic field, namely, that the typical field-induced sharp double-peak structure in the low-temperature behavior of the specific heat capacity, which is directly related to the very existence of the highly macroscopically degenerated single-point ground states, disappears already for relatively large values of the temperature.
Abstract. The antiferromagnetic spin-1/2 Ising model with the presence of the multisite interaction and in the external magnetic field on the infinite tetrahedral chain is solved exactly by using the transfer matrix method. Using the exact expression for the free energy per site of the model the thermodynamic properties of the model are investigated in detail. It is shown that the total magnetisation per site forms the magnetisation plateaus at low temperatures, the properties of which depend on the strength of the multisite interaction. The set of all possible ground states is found and discussed. The existence of the so-called single-point ground states is shown and their properties are studied in detail. The entropy per site of the model is investigated and the exact expressions for the residual entropies of all ground states are found and their macroscopic degeneracies are discussed. The existence of the ground states with the same value of magnetisation but with different entropies is observed. In addition, the behaviour of the susceptibility and the specific heat is also studied.
In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds
J1 and competing antiferromagnetic basal bonds
J2. At a quantum phase transition point
∣J2/J1∣=1/2, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value
limT→∞S(T)/N=ln2. In the present paper we study in detail the role of the spin quantum number
s and the magnetic field
H in the parameter region around the transition (flat-band) point. For that we use full exact diagonalization up to
N=20 lattice sites and the finite-temperature Lanczos method up to
N=36 sites to calculate the density of states as well as the temperature dependence of the specific heat, the entropy and the susceptibility. The study of chain lengths up to
N=36 allows a careful finite-size analysis. At the flat-band point we find extremely small finite-size effects for spin
s=1/2, i.e., the numerical data virtually correspond to the thermodynamic limit. In all other cases the finite-size effects are still small and become visible at very low temperatures. In a sizeable parameter region around the flat-band point the former massively degenerate ground-state manifold acts as a large manifold of low-lying excitations leading to extraordinary thermodynamic properties at the transition point as well as in its vicinity such as an additional low-temperature maximum in the specific heat. Moreover, there is a very strong influence of the magnetic field on the low-temperature thermodynamics including an enhanced magnetocaloric effect.
We consider the antiferromagnetic spin-1/2 Ising model with multisite interaction in an external magnetic field on an infinite zigzag ladder. The model is solved exactly by using the transfer matrix method. Using the exact expression for the total magnetization per site, the magnetic properties of the model are investigated in detail. The model exhibits the formation of magnetization plateaus for low temperatures, and it is shown that their properties depend strongly on the strength of the multisite interaction. All possible ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found. The macroscopic degeneracy of the ground states is investigated and discussed.
Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg
S=21 spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of
L=200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multiparticle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.
Abstract The influence of the single-ion anisotropy on the thermodynamic properties of ferromagnetic as well as ferrimagnetic spin-1/2 − 1 mixed systems on the square and simple cubic lattice is investigated in the framework of the exactly solvable Ising-like models on the corresponding recursive lattices. The exact solutions of the models are present in the form of the explicit expressions for the free energy per site as the functions of the coordinates of the fixed points of the corresponding systems of recursion relations. The phase diagrams of the models are determined and the existence of compensation temperatures in the ferrimagnetic cases are discussed. The equations that drive the positions of the critical points are derived. The existence of the tricritical behavior in the three-dimensional system on the simple cubic lattice and its nonexistence in the case of the two-dimensional system on the square lattice is demonstrated. It is shown that the presence of the single-ion anisotropy can naturally lead to the emergence of the thermodynamic anomalies typical for frustrated magnetic systems even in unfrustrated ferromagnetic systems on studied bipartite lattices. First of all, the studied models exhibit the formation of strict residual-entropy hierarchies between the neighboring ground states of the system of three different ground states. It is also shown that due to this behavior of the entropy the specific heat capacity of the models exhibit anomalous (Schottky) behavior at low temperatures in the vicinity of the values of the anisotropy parameter, for which highly macroscopically degenerated single-point-like ground states are formed.
The exactly solvable spin-1/2 Ising-Heisenberg distorted diamond chain in the presence of the external magnetic field is investigated for the case of antiferromagnetic Ising and ferromagnetic XXZ Heisenberg interactions. The influence of quantum fluctuations and the distortion on the ground state, magnetic and thermal properties of the model are studied in detail.In particular, it is established that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and 1/3 of the saturation magnetization. It is demonstrated that the temperature dependence of the specific heat reveals up to four distinct peaks at zero magnetic field and up to five distinct peaks at a weak magnetic field. The physical origin of all observed additional peaks of the specific heat has been clarified on the grounds of dominating thermal excitations. We have shown that the quantum fluctuations give rise to an effective geometrical frustration in this chain.