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

QCD Viscosity to Entropy Density Ratio in the Hadronic Phase

Shear viscosity (eta) of QCD in the hadronic phase is computed by the coupled Boltzmann equations of pions and nucleons in low temperatures and low baryon number densities. The eta to entropy density ratio eta/s maps out the nuclear gas-liquid phase transition by forming a valley tracing the phase transition line in the temperature-chemical potential plane. When the phase transition turns into a crossover, the eta/s valley gradually disappears. We suspect the general feature for a first-order phase transition is that eta/s has a discontinuity in the bottom of the eta/s valley. The discontinuity coincides with the phase transition line and ends at the critical point. Beyond the critical point, a smooth eta/s valley is seen. However, the valley could disappear further away from the critical point. The eta/s measurements might provide an alternative to identify the critical points.Comment: 16 pages, 4 figures. Minor typos corrected and references adde

S and D Wave Mixing in High TcT_c Superconductors

For a tight binding model with nearest neighbour attraction and a small orthorhombic distortion, we find a phase diagram for the gap at zero temperature which includes three distinct regions as a function of filling. In the first, the gap is a mixture of mainly $d$-wave with a smaller extended $s$-wave part. This is followed by a region in which there is a rapid increase in the $s$-wave part accompanied by a rapid increase in relative phase between $s$ and $d$ from 0 to $\pi$. Finally, there is a region of dominant $s$ with a mixture of $d$ and zero phase. In the mixed region with a finite phase, the $s$-wave part of the gap can show a sudden increase with decreasing temperature accompanied with a rapid increase in phase which shows many of the characteristics measured in the angular resolved photoemission experiments of Ma {\em et al.} in $\rm Bi_2Sr_2CaCu_2O_8$Comment: 12 pages, RevTeX 3.0, 3 PostScript figures uuencoded and compresse

Quantum effective potential for U(1) fields on S^2_L X S^2_L

We compute the one-loop effective potential for noncommutative U(1) gauge fields on S^2_L X S^2_L. We show the existence of a novel phase transition in the model from the 4-dimensional space S^2_L X S^2_L to a matrix phase where the spheres collapse under the effect of quantum fluctuations. It is also shown that the transition to the matrix phase occurs at infinite value of the gauge coupling constant when the mass of the two normal components of the gauge field on S^2_L X S^2_L is sent to infinity.Comment: 13 pages. one figur

Nature of phase transition(s) in striped phase of triangular-lattice Ising antiferromagnet

Different scenarios of the fluctuation-induced disordering of the striped phase which is formed at low temperatures in the triangular-lattice Ising model with the antiferromagnetic interaction of nearest and next-to-nearest neighbors are analyzed and compared. The dominant mechanism of the disordering is related to the formation of a network of domain walls, which is characterized by an extensive number of zero modes and has to appear via the first-order phase transition. In principle, this first-order transition can be preceded by a continuous one, related to the spontaneous formation of double domain walls and a partial restoration of the broken symmetry, but the realization of such a scenario requires the fulfillment of rather special relations between the coupling constants.Comment: 10 pages, 7 figures, ReVTeX

Phase transition(s) in finite density QCD

The Grand Canonical formalism is generally used in numerical simulations of finite density QCD since it allows free mobility in the chemical potential $\mu$. We show that special care has to be used in extracting numerical results to avoid dramatic rounding effects and spurious transition signals. If we analyze data correctly, with reasonable statistics, no signal of first order phase transition is present and results using the Glasgow prescription are practically coincident with the ones obtained using the modulus of the fermionic determinant.Comment: 6 pages, 5 ps figs. To appear in Proceedings of "QCD at Finite Baryon Density" workshop, Bielefeld, 27-30 April 199

Phase Diagrams of S=3/2, 2 XXZ Spin Chains with Bond-Alternation

We study the phase diagram of S=3/2 and S=2 bond-alternating spin chains numerically. In previous papers, the phase diagram of S=1 XXZ spin chain with bond-alternation was shown to reflect the hidden $Z_{2}\times Z_{2}$ symmetry. But for the higher S Heisenberg spin chain, the successive dimerization transition occurs, and for anisotropic spin chains the phase structure will be more colorful than the S=1 case. Using recently developed methods, we show directly that the phase structure of the anisotropic spin chains relates to the $Z_{2}\times Z_{2}$ symmetry.Comment: 13 pages, 6 figures(eps), RevTe