Phase transitions in classical and quantum spin systems

Classical and quantum spin systems are widely used models in both experimental and theoretical condensed matter physics. In many materials, the electronic interactions can be difficult to model exactly. However, in some insulators (Mott insulators), the magnetic (spin) interactions can be captured well with spin-only models. Several models are studied in this thesis. First, I report the solution of a long-standing issue in a classical frustrated spin model (i.e., where the quantum effects are neglected and the complexity is due to competing interactions): the nature of the thermal phase transition to a stripe state in the two dimensional (2D) J1-J2 model. Here J1 and J2 are nearest- and next-nearest-neighbor couplings. Monte Carlo simulations with single-spin updates are used for the calculations, and an extended-ensemble method, a generalization of the Wang-Landau algorithm, is also developed and tested. I focus on the study of "weak universality" behavior (continuously varying critical exponents, with one of the exponents staying fixed), for which I show a correspondence with a known class of conformal field theories with charge c = 1. Next, moving to quantum spins, to shed light on magnetic systems studied experimentally and to investigate new types of quantum states of interest in developing theories of quantum magnetism, I study the S = 1/2 Heisenberg model on the 2D square lattice with added six-spin interactions (the so-called J-Q3 model) as well as a set of 3D quantum antiferromagnets on dimerized lattices. Here I use the stochastic series expansion quantum Monte Carlo method. In the study of the J-Q3 model, I report on a similar weak-universality behavior as in the classical J1-J2 model, but with a mapping to a different known class of c = 1 conformal field theories. The critical behavior of the system again shows continuously changing exponents, in a way which corresponds to a gradual weakening of Z4 symmetry-breaking to an emergent U(1) symmetry. In the study of dimerized antiferromagnets, I report on a universal behavior of the Néel temperature TN, which can be related to ground state parameters independently of the microscopic interaction details in several different models

Phase transitions in the frustrated Ising model on the square lattice

We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1<0 (nearest neighbor, ferromagnetic) and J2 >0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g=J2/|J1|>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2<g<g*, where g* = 0.67(1). Thereafter, the transitions from g above g* are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g* in the J1-J2 model. The continuous transitions near g* can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g>1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological bench-marks for weakly first-order behaviors and Ashkin-Teller criticality.Comment: 13 pages, 13 figure

Universal Neel Temperature in Three-Dimensional Quantum Antiferromagnets

We study three-dimensional dimerized S=1/2 Heisenberg antiferromagnets, using quantum Monte Carlo simulations of systems with three different dimerization patterns. We propose a way to relate the N\'eel temperature T_N to the staggered moment m_s of the ground state. Mean-field arguments suggest that T_N is proportional to m_s close to a quantum-critical point. We find an almost perfect universality (including the prefactor) if T_N is normalized by a proper lattice-scale energy. We show that the temperature T* at which the magnetic susceptibility has a maximum is a good choise, i.e., T_N/T* versus m_s is a universal function (also beyond the linear regime). These results are useful for analyzing experiments on systems where the spin couplings are not known precisely, e.g., TlCuCl3.Comment: 5 pages, 5 figure

Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice

We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J1<0 (nearest-neighbor, ferromagnetic) and J2>0 (second-neighbor, antiferromagnetic) for g=J2/|J1|>1/2. Using Monte Carlo simulations and known analytical results, we demonstrate Ashkin-Teller criticality for g>= g*, i.e., the critical exponents vary continuously between those of the 4-state Potts model at g=g* and the Ising model for g -> infinity. Thus, stripe transitions offer a route to realizing a related class of conformal field theories with conformal charge c=1 and varying exponents. The transition is first-order for g<g*= 0.67(1), much lower than previously believed, and exhibits pseudo first-order behavior for g* < g < 1.Comment: 5 pages, 5 figure

Effect of thoracolumbar fascia injury on reported outcomes after percutaneous vertebroplasty

PurposeThoracolumbar fascia injury is often associated with poor early pain relief after percutaneous vertebroplasty (PVP). This study will evaluate the effects of thoracolumbar fascia injury on early pain relief and time to get out of bed after PVP.MethodsA total of 132 patients treated with PVP for osteoporotic vertebral compression fractures (OVCF) were included and divided into injured group (52 cases) and non-injured group (80 cases) according to the existence of thoracolumbar fascia injury. Before surgery, 1 day, 3 days, 1 week, 1 month, and 3 months after surgery, and at the last follow-up, the primary patient-reported outcome measures (PROMs) were the visual analogue scale (VAS) of pain while rolling over and standing, and the secondary PROMs was the Oswestry disability index (ODI). Meanwhile, the achieved rate of minimal clinically important differences (MCID) and patient acceptable symptom states (PASS) of the above measures in both groups was evaluated at the last follow-up.ResultsExcept for the postoperative 3 months and the last follow-up, there were statistically significant differences in VAS-standing and ODI between the two groups at other time points after surgery (P &lt; 0.05), and the non-injured group was significantly better than the injured group. At the last follow-up, there was no statistically significant difference in the MCID and PASS achievement rates of the above measures between the two groups (P &gt; 0.05). In addition, the proportion of patients who got out of bed 1 and 3 days after surgery in the non-injury group was significantly higher than that in the injury group (P = 0.000 for both).ConclusionThoracolumbar fascia injury significantly affected early pain relief and extended time of getting out of bed after PVP. Attention should be paid to preoperative evaluation of thoracolumbar fascial injury in order to better predict the postoperative efficacy of PVP

Modelling and assessment of pneumatic artificial muscle

The pneumatic artificial muscle (PAM) being a new type of actuator is widespread used in engineering field because it possesses the attractive attributes of safe operation, low cost, high output force to volume. It is a prime requirement to establish an effective theoretical model to predict the performance of the PAM as well as other actuators. In this paper a new PAM model is established by employing conservation energy and the Mooney-Rivlin strain energy function for the rubber of PAM. This model is compared with the previous models and the experimental results and it shows that the model truly improves the assessment of forces and contraction that can be achieved by the PAM. However, the significant discrepancy still exists between the theoretical model and the experiment. A number of factors, like friction force, which result in the discrepancy are discusse

Ag-Decorated ATaO₃ (A = K, Na) Nanocube Plasmonic Photocatalysts with Enhanced Photocatalytic Water-Splitting Properties

Tantalate semiconductor nanocrystals have been at the forefront of the photocatalytic conversion of solar energy to supply hydrogen owing to their favorable and tunable optical and electronic properties as well as advances in their synthesis. However, a narrow band gap is required for response to improve the efficiency of the photocatalysts. Here we propose an efficient enhancement of the H₂ generation under simulated sunlight and visible light irradiation by a dispersion of Ag-decorated KTaO₃ and NaTaO₃ nanocubes. X-ray diffraction and UV–vis diffuse reflectance spectra are used to characterize the products. Transmission electron microscope (TEM) and high-resolution high-angle annular dark-field scanning TEM (HAADF-STEM) images show that the Ag nanoparticles (NPs) are uniformly loaded on the surfaces of KTaO₃ and NaTaO₃. The photocatalytic water-splitting results over Ag-decorated KTaO₃ and NaTaO₃ show that the rate for H₂ evolution from aqueous CH₃OH solutions is up to 185.60 and 3.54 μmol/h·g under simulated sunlight and the rate for H₂ evolution is more than 2 times than that of pure NaTaO₃ and KTaO₃ materials. However, under purely visible light illumination the highest H₂ evolution of 25.94 and 0.83 μmol/h·g is observed in the case of Ag-decorated KTaO₃ and NaTaO₃ nanocubes. To the best of our knowledge, this is the first time that the photocatalytic water-splitting activity of the prepared Ag-decorated KTaO₃ and NaTaO₃ nanocubes has been reported