Effects of third-neighbor interactions on the frustrated quantum Ising model.

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Enhancement of the magnetocaloric effect in geometrically frustrated cluster spin glass systems.

In this work, we theoretically demonstrate that a strong enhancement of the magnetocaloric effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy.

Thermally driven state in a spin-1 model with competing interactions.

We study a recently proposed spin-1 model with competing antiferromagnetic first-neighbor interaction and a third-neighbor coupling mediated by nonmagnetic states, which reproduces topological features of the phase diagrams of high-T_{c} superconductors [S. A. Cannas and D. A. Stariolo, Phys. Rev. E 99, 042137 (2019)2470-004510.1103/PhysRevE.99.042137]. We employ a cluster mean-field approach to investigate effects of crystal field anisotropy on the phase transitions hosted by this model. At low temperatures, the temperature-crystal field phase diagram exhibits superantiferromagnetic (SAF), antiferromagnetic (AF), and paramagnetic (PM) phases. In addition, we found a thermally driven state between SAF and PM phases. This thermally driven state and the SAF phase appears in the phase diagram as a domelike structure. Our calculations indicate that only second-order phase transitions occur in the PM-AF phase boundary, as suggested by previous Monte Carlo simulations.

Transverse field effects on the competition between antiferromagnetic and cluster spin-glass phases.

We investigate a disordered cluster Ising antiferromagnet in the presence of a transverse field. By adopting a replica cluster mean-field framework, we analyze the role of quantum fluctuations in a model with competing short-range antiferromagnetic and intercluster disordered interactions. The model exhibits paramagnetic (PM), antiferromagnetic (AF), and cluster spin-glass (CSG) phases, which are separated by thermal and quantum phase transitions. A scenario of strong competition between AF and CSG unveils a number of interesting phenomena induced by quantum fluctuations, including a quantum PM state and quantum driven criticality. The latter occurs when the thermally driven PM-AF discontinuous phase transition becomes continuous at strong transverse fields. Analogous phenomena have been reported in a number of systems, but a description of underlying mechanisms is still required. Our results indicate that quantum driven criticality can be found in a highly competitive regime of disordered antiferromagnets, which is in consonance with recent findings in spin models with competing interactions.

Field-induced glassy state in disordered cluster antiferromagnets.

We investigate the role of antiferromagnetic spin clusters on the glassiness induced by uniform and random fields. We consider an antiferromagnetic disordered model that is treated within the replica method, resulting in an effective single-cluster problem. Our results show that regimes of weak and intermediate disorder are suitable for highly unusual phenomena. For the case of a uniform field, cluster polarization can favor a cluster spin-glass state, i.e. the magnetic field increases the freezing temperature at intermediate disorders. In addition, random fields introduce local perturbations that allow uncompensated cluster states, supporting cluster freezing even at very weak disorders. The theoretical framework presented here can be useful for the understanding of phenomena observed in magnetic glassy systems that have spin clusters as building blocks instead of individual spins. In particular, we suggest that our results can help to explain the magnetic behaviour of the rare earth TbIn0.99Mn0.01O3, which has been recently proposed to be composed of antiferromagnetic clusters, presenting a field-induced increase of the freezing temperature.

Quantum Ising model on the frustrated square lattice.

We investigate the role of a transverse field on the Ising square antiferromagnet with first (J_{1}) and second (J_{2}) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio J_{2}/J_{1} in possible experimental realizations of the quantum J_{1}-J_{2} Ising antiferromagnet.

Spin liquid and infinitesimal-disorder-driven cluster spin glass in the kagome lattice.

The interplay between geometric frustration (GF) and bond disorder is studied in the Ising kagome lattice within a cluster approach. The model considers antiferromagnetic short-range couplings and long-range intercluster disordered interactions. The replica formalism is used to obtain an effective single cluster model from where the thermodynamics is analyzed by exact diagonalization. We found that the presence of GF can introduce cluster freezing at very low levels of disorder. The system exhibits an entropy plateau followed by a large entropy drop close to the freezing temperature. In this scenario, a spin-liquid (SL) behavior prevents conventional long-range order, but an infinitesimal disorder picks out uncompensated cluster states from the multi-degenerate SL regime, potentializing the intercluster-disordered coupling and bringing the cluster spin-glass state. To summarize, our results suggest that the SL state combined with low levels of disorder can activate small clusters, providing hypersensitivity to the freezing process in geometrically frustrated materials and playing a key role in the glassy stabilization. We propose that this physical mechanism could be present in several geometrically frustrated materials. In particular, we discuss our results in connection with the recent experimental investigations of the Ising kagome compound Co3Mg(OH)6Cl2.

Quantum correlated cluster mean-field theory applied to the transverse Ising model.

Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

Effect of geometrical frustration on inverse freezing.

The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor (J_{1}) and second-neighbor (J_{2}) intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings (J) among clusters. We obtain phase diagrams of temperature versus J_{1}/J in two cases: the absence of J_{2} interaction and the isotropic limit J_{2}=J_{1}, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J_{1}/J in both cases. The J_{1} interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF.

Interplay between spin-glass clusters and geometrical frustration.

The presence of spin-glass (SG) order in highly geometrically frustrated systems is analyzed in a cluster SG model. The model considers infinite-range disordered interactions among cluster magnetic moments and the J(1)-J(2) model couplings between Ising spins of the same cluster. This model can introduce two sources of frustration: one coming from the disordered interactions and another coming from the J(1)-J(2) intracluster interactions (intrinsic frustration). The framework of one-step replica symmetry breaking is adopted to obtain a one-cluster problem that is exactly solved. As a main result we create phase diagrams of the temperature T versus intensity of the disorder J, where the paramagnetic-SG phase transition occurs at T(f) when T decreases for high-J values. For low-J values, the SG order is absent for antiferromagnetic clusters without intrinsic frustration. However, the SG order can be observed within the intracluster intrinsic frustration regime even for lower intensity of disorder. In particular, the results indicate that the presence of small clusters in geometrically frustrated antiferromagnetic systems can help stabilize the SG order within a weak disorder.

Correlated cluster mean-field theory for spin-glass systems.

The competition between cluster spin glass (CSG) and ferromagnetism or antiferromagnetism is studied in this work. The model considers clusters of spins with short-range ferromagnetic or antiferromagnetic (FE-AF) interactions (J_{0}) and long-range disordered couplings (J) between clusters. The problem is treated by adapting the correlated cluster mean-field theory of D. Yamamoto [Phys. Rev. B 79, 144427 (2009)]. Phase diagrams T/J×J_{0}/J are obtained for different cluster sizes n_{s}. The results show that the CSG phase is found below the freezing temperature T_{f} for lower intensities of J_{0}/J. The increase of short-range FE interaction can favor the CSG phase, while the AF one reduces the CSG region by decreasing the T_{f}. However, there are always critical values of J_{0} where AF or FE orders become stable. The results also indicate a strong influence of the cluster size in the competition of magnetic phases. For AF cluster, the increase of n_{s} diminishes T_{f} reducing the CSG phase region, which indicates that the cluster surface spins can play an important role in the CSG arising.

Spin-1 Hopfield model under a random field.

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

Inverse freezing in a cluster Ising spin-glass model with antiferromagnetic interactions.

Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.

Inverse freezing in the Ghatak-Sherrington model with a random field.

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from the GS model without a RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field D, is gradually suppressed when the RF is increased.

The van Hemmen-Kondo model for disordered cerium systems.

The interplay between disorder and strong correlations has been observed experimentally in disordered cerium alloys such as Ce(Ni, Cu) or Ce(Pd, Rh). In the case of Ce(Ni, Cu) alloys with a Cu concentration x between 0.6 and 0.3, the first studies have shown a smooth transition with decreasing temperature from a spin glass phase to ferromagnetism; for x smaller than 0.2, a Kondo phase has been observed. The situation is more complicated now due to the recent observation of magnetic clusters. The competition between the Kondo effect, the spin glass (SG) and the ferromagnetic (FE) ordering has been extensively studied theoretically. The Kondo effect is described by the usual mean-field approximation; we have treated the SG behavior successively by the Sherrington-Kirkpatrick model, then by the Mattis model and finally by the van Hemmen model, which takes both a ferromagnetic part and a site-disorder random part for the intersite exchange interaction. We present here the results obtained by the van Hemmen-Kondo model: for a large Kondo exchange JK, a Kondo phase is obtained while, for smaller JK, the succession of an SG phase, a mixed SG-FE one and finally an FE one has been obtained with decreasing temperature. This model improves the theoretical description of disordered Kondo systems by providing a simpler approach for further calculations of magnetic clusters and can, therefore, account for recent experimental data on disordered cerium systems.