31 research outputs found

    Extension to order ÎČ23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

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    Using a renormalized linked-cluster-expansion method, we have extended to order ÎČ23\beta^{23} the high-temperature series for the susceptibility χ\chi and the second-moment correlation length Ο\xi of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of χ\chi and Ο\xi. Our best estimates for the inverse critical temperatures are ÎČcsc=0.221654(1)\beta^{sc}_c=0.221654(1) and ÎČcbcc=0.1573725(6)\beta^{bcc}_c=0.1573725(6). For the susceptibility exponent we get Îł=1.2375(6)\gamma=1.2375(6) and for the correlation length exponent we get Îœ=0.6302(4)\nu=0.6302(4). The ratio of the critical amplitudes of χ\chi above and below the critical temperature is estimated to be C+/C−=4.762(8)C_+/C_-=4.762(8). The analogous ratio for Ο\xi is estimated to be f+/f−=1.963(8)f_+/f_-=1.963(8). For the correction-to-scaling amplitude ratio we obtain aΟ+/aχ+=0.87(6)a^+_{\xi}/a^+_{\chi}=0.87(6).Comment: Misprints corrected, 8 pages, latex, no figure

    Critical exponents and equation of state of the three-dimensional Heisenberg universality class

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    We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.

    Practical Immutable Signature Bouquets (PISB) for Authentication and Integrity in Outsourced Databases

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    Abstract. Database outsourcing is a prominent trend that enables organizations to offload their data management overhead (e.g., query handling) to the external service providers. Immutable signatures are ideal tools to provide authentication and integrity for such applications with an important property called immutability. Signature immutability ensures that, no attacker can derive a valid signature for unposed queries from previous queries and their corresponding signatures. This prevents an attacker from creating his own de-facto services via such derived signatures. Unfortunately, existing immutable signatures are very computation and communication costly (e.g., highly interactive), which make them impractical for task-intensive and heterogeneous applications. In this paper, we developed two new schemes that we call Practical and Immutable Signature Bouquets (PISB), which achieve efficient immutability for outsourced database systems. Both PISB schemes are very simple, noninteractive, and computation/communication efficient. Our generic scheme can be constructed from any aggregate signature coupled with a standard signature. Hence, it can flexibly provide performance trade-offs for various types of applications. Our specific scheme is constructed from Condensed-RSA and Sequential Aggregate RSA. It has a very low verifier computational overhead and end-to-end delay with a small signature size. We showed that PISB schemes are secure and also much more efficient than previous alternatives
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