Thermodynamic properties and phase diagrams of spin-1 quantum Ising systems with three-spin interactions

The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable, metastable and unstable branches of the order parameters are obtained. According to the stable conditions at critical point, we find that the systems exhibit tricritical points. With crystal field and biquadratic interactions, the system has rich phase diagrams with single reentrant or double reentrant phase transitions for appropriate ranges of the both parameters.Comment: 10 pages, 5 figure

Fast and Simple Mixture of Softmaxes with BPE and Hybrid-LightRNN for Language Generation

Mixture of Softmaxes (MoS) has been shown to be effective at addressing the expressiveness limitation of Softmax-based models. Despite the known advantage, MoS is practically sealed by its large consumption of memory and computational time due to the need of computing multiple Softmaxes. In this work, we set out to unleash the power of MoS in practical applications by investigating improved word coding schemes, which could effectively reduce the vocabulary size and hence relieve the memory and computation burden. We show both BPE and our proposed Hybrid-LightRNN lead to improved encoding mechanisms that can halve the time and memory consumption of MoS without performance losses. With MoS, we achieve an improvement of 1.5 BLEU scores on IWSLT 2014 German-to-English corpus and an improvement of 0.76 CIDEr score on image captioning. Moreover, on the larger WMT 2014 machine translation dataset, our MoS-boosted Transformer yields 29.5 BLEU score for English-to-German and 42.1 BLEU score for English-to-French, outperforming the single-Softmax Transformer by 0.8 and 0.4 BLEU scores respectively and achieving the state-of-the-art result on WMT 2014 English-to-German task

Thermal entanglement between non-nearest-neighbor spins on fractal lattices

We investigate thermal entanglement between two non-nearest-neighbor sites in ferromagnetic Heisenberg chain and on fractal lattices by means of the decimation renormalization-group (RG) method. It is found that the entanglement decreases with increasing temperature and it disappears beyond a critical value T_{c}. Thermal entanglement at a certain temperature first increases with the increase of the anisotropy parameter {\Delta} and then decreases sharply to zero when {\Delta} is close to the isotropic point. We also show how the entanglement evolves as the size of the system L becomes large via the RG method. As L increases, for the spin chain and Koch curve the entanglement between two terminal spins is fragile and vanishes when L\geq17, but for two kinds of diamond-type hierarchical (DH) lattices the entanglement is rather robust and can exist even when L becomes very large. Our result indicates that the special fractal structure can affect the change of entanglement with system size.Comment: 10 pages, 6 figure

IRCI Free Range Reconstruction for SAR Imaging with Arbitrary Length OFDM Pulse

Our previously proposed OFDM with sufficient cyclic prefix (CP) synthetic aperture radar (SAR) imaging algorithm is inter-range-cell interference (IRCI) free and achieves ideally zero range sidelobes for range reconstruction. In this OFDM SAR imaging algorithm, the minimum required CP length is almost equal to the number of range cells in a swath, while the number of subcarriers of an OFDM signal needs to be more than the CP length. This makes the length of a transmitted OFDM sequence at least almost twice of the number of range cells in a swath and for a wide swath imaging, the transmitted OFDM pulse length becomes long, which may cause problems in some radar applications. In this paper, we propose a CP based OFDM SAR imaging with arbitrary pulse length, which has IRCI free range reconstruction and its pulse length is independent of a swath width. We then present a novel design method for our proposed arbitrary length OFDM pulses. Simulation results are presented to illustrate the performances of the OFDM pulse design and the arbitrary pulse length CP based OFDM SAR imaging.Comment: 29 pages, 10 figures, regular pape

In an Attempt to Introduce Long-range Interactions into Small-world Networks

Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Guassian model built on two typical Small-world Networks (SWNs) is studied. The results show much difference from the classical case, and thus may induce some more accurate discussion on the critical properties of the spin-lattice systems combined with the SWNs.Comment: 4 pages, 3 figures, 18 referenc