The tensor renormalization group study of the general spin-S Blume-Capel model

We focus on the special situation of $D=2J$ of the general spin-S Blume-Capel model on the square lattice. Under the infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are discussed by the newly developed tensor renormalization group method. For the case of the integer spin-S, the system will undergo $S$ first-order phase transitions with the successive symmetry breaking with the magnetization $M=S,S-1,...0$. For the half-integer spin-S, there are similar $S-1/2$ first order phase transition with $M=S,S-1,...1/2$ stepwise structure, in addition, there is a continuous phase transition due to the spin-flip $Z_2$ symmetry breaking. In the low temperature regions, all first-order phase transitions are accompanied by the successive disappearance of the optional spin-component pairs($s,-s$), furthermore, the critical temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of the magnetic field, the visualization parameter characterizing the intrinsic degeneracy of the different phases clearly demonstrates the phase transition process.Comment: 6 pages, 7 figure

Exact solutions of a class of S=1 quantum Ising spin models

We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising models, characterized by the total number of holes. A recursion formula is derived for the partition function based on the reduced $S=1/2$ Ising model. This simplifies greatly the summation over all the hole configurations. It allows the thermodynamic quantities to be rigorously determined in the thermodynamic limit. The ground state phase diagram is determined for both the uniform and dimerized spin chains. The corresponding thermodynamic properties are calculated and discussed.Comment: 11 pages, 9 figures, published versio

Adiabatic approximation in the ultrastrong-coupling regime of a system consisting of an oscillator and two qubits

We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyse the system by the adiabatical approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Energy-level spectrum of the system in the adiabatical displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution.Comment: 13pages,4 figure

Multi-wavelength study of the supernova remnant Kes 79 (G33.6+0.1): On its supernova properties and expansion into a molecular environment

Kes 79 (G33.6+0.1) is an aspherical thermal composite supernova remnant (SNR) observed across the electromagnetic spectrum and showing an unusual highly-structured morphology, in addition to harboring a central compact object (CCO). Using the CO J=1-0, J=2-1, and J=3-2 data, we provide the first direct evidence and new morphological evidence to support the physical interaction between the SNR and the molecular cloud at $V_LSR\sim 105$ km s$^{-1}$. We revisit the 380 ks XMM-Newton observations and perform a dedicated spatially resolved X-ray spectroscopic study with careful background subtraction. The overall X-ray-emitting gas is characterized by an under-ionized ($\tau_c \sim 6\times 10^{11}$ cm^${-3}$) cool ($kT_c \approx 0.20$ keV) plasma with solar abundances, plus an under-ionized ($\tau_h\sim 8\times 10^{10}$ cm$^{-3}$) hot ($kT_h\approx 0.80$ keV) plasma with elevated Ne, Mg, Si, S and Ar abundances. Kes 79 appears to have a double-hemisphere morphology viewed along the symmetric axis. Projection effect can explain the multiple shell structures and the thermal composite morphology. The X-ray filaments, spatially correlated with the 24 um IR filaments, are suggested to be due to the SNR shock interaction with dense gas, while the halo forms from SNR breaking out into a tenuous medium. The high-velocity, hot ($kT_h\sim 1.4$--1.6 keV) ejecta patch with high metal abundances, together with the non-uniform metal distribution across the SNR, indicating an asymmetric SN explosion of Kes 79. We refine the Sedov age to 4.4--6.7 kyr and the mean shock velocity to 730 km s$^{-1}$. Our multi-wavelength study suggests a progenitor mass of $\sim 15$--20 solar masses for the core-collapse explosion that formed Kes 79 and its CCO, PSR J1852+0040.Comment: 17 pages, 12 figures, 3 tables, published in Ap