Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

Recently, we developed and implemented the bond propagation algorithm for calculating the partition function and correlation functions of random bond Ising models in two dimensions. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function, and we derive explicit expressions for this transformation. We also discuss variations of the original bond propagation procedure within the larger context of Y-Delta-Y-reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.Comment: 12 pages, 10 figures; submitte

The cosmic QCD phase transition with dense matter and its gravitational waves from holography

Consistent with cosmological constraints, there are scenarios with the large lepton asymmetry which can lead to the finite baryochemical potential at the cosmic QCD phase transition scale. In this paper, we investigate this possibility in the holographic models. Using the holographic renormalization method, we find the first order Hawking-Page phase transition, between Reissner-Nordstr$\rm\ddot{o}$m AdS black hole and thermal charged AdS space, corresponding to the de/confinement phase transition. We obtain the gravitational wave spectra generated during the evolution of bubbles for a range of the bubble wall velocity and examine the reliability of the scenarios and consequent calculations by gravitational wave experiments.Comment: 18 pages , 4 figures, references and new discussions added, accepted to be published in Phys. Lett.