We present three-dimensional simulations of the dynamics of binary neutron star mergers from the late stage of the inspiral process up to $\sim 20\mathrm{ms}$ after the system has merged, either to form a hypermassive neutron star or a rotating black hole. We investigate five equal mass models of total gravitational mass 2.207, 2.373, 2.537, 2.697, and $2.854M_{\odot }$, respectively, and four unequal mass models with $M_{\mathrm{ADM}}\simeq 2.53M_{\odot }$ and $q\simeq 0.94$, 0.88, 0.83, and 0.77 (where $q=M^{(1)}/M^{(2)}$ is the mass ratio). We use a semirealistic equation of state, namely, the seven-segment piecewise polytropic SLyPP with a thermal component given by ${\mathrm{\Gamma }}_{\text{th}}=1.8$. We have also compared the resulting dynamics (for one model) using both the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector and also different reconstruction methods for the matter sector, namely, PPM, WENO, and MP5. Our results show agreement at high resolution, but superiority of BSSN-NOK supplemented by WENO reconstruction at lower resolutions. One of the important characteristics of the present investigation is that for the first time it has been done using only publicly available open source software: the Einstein Toolkit code, deployed for the dynamical evolution, and the LORENE code, for the generation of the initial models. All of the source code and parameters used for the simulations have been made publicly available. This not only makes it possible to rerun and reanalyze our data but also enables others to directly build upon this work for future research.

We present a study of the deconfinement phase transition of one-flavor QCD using the multiboson algorithm. The mass of the Wilson fermions relevant for this study is moderately large and the non-Hermitian multiboson method is a superior simulation algorithm. Finite-size scaling is studied on lattices of size $8^3\times 4,$ ${12}^3\times 4$, and ${16}^3\times 4$. The behaviors of the peak of the Polyakov loop susceptibility, the deconfinement ratio, and the distribution of the norm of the Polyakov loop are all characteristic of a first-order phase transition for heavy quarks. As the quark mass decreases, the first-order transition gets weaker and turns into a crossover. To investigate finite-size scaling on larger spatial lattices we use an effective action in the same universality class as QCD. This effective action is constructed by replacing the fermionic determinant with the Polyakov loop identified as the most relevant $Z\left(3\right)\mathrm{}$-symmetry-breaking term. Higher-order effects are incorporated in an effective $Z\left(3\right)\mathrm{}$-breaking field h, which couples to the Polyakov loop. Finite-size scaling determines the value of h where the first-order transition ends. Our analysis at the end point $h_{\mathrm{ep}}$ indicates that the effective model and thus QCD are consistent with the universality class of the three-dimensional Ising model. Matching the field strength at the end point $h_{\mathrm{ep}}$ to the $\kappa$ values used in the dynamical quark simulations we estimate the end point ${\kappa }_{\mathrm{ep}}$ of the first-order phase transition. We find ${\kappa }_{\mathrm{ep}}\sim 0.08$ which corresponds to a quark mass of about 1.4 GeV.

We study the transverse quantum ANNNI model in the region of high frustration (k>0.5) using the DMRG algorithm. We obtain a precise determination of the phase diagram, showing clear evidence for the existence of a floating phase, separated from the paramagnetic modulated phase by a high-order critical line ending at the multicritical point. We obtain simple and accurate formulae for the two critical lines.Comment: 20 pages, 16 figures. Major revision: numerical evidence improved, presentation clarified, discussion on KT phase transitions added, references update