We develop a symmetric teleparallel gravity model in a space-time with only the nonmetricity is nonzero, in terms of a Lagrangian quadratic in the non-metricity tensor. We present a detailed discussion of the variations that may be used for any gravitational formulation. We seek Schwarzschild-type solutions because of its observational significance and obtain a class of solutions that includes Schwarzschild-type, Schwarzschild-de Sitter-type and ReissnerNordström-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions.
In this paper we elaborate on the symmetric teleparallel gravity (STPG) written in a nonRiemannian spacetime with nonzero nonmetricity, but zero torsion and zero curvature.Firstly we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry the autoparallel curves coincides with those of the Riemannian spacetimes. Subsequently we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our lagrangian is equivalent to the Einstein-Hilbert lagrangian for certain values of coupling coefficients. Thus we arrive at calculating the field equations via independent variations. Then we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally we discuss a minimal coupling of a spin-1/2 field to STPG.
The five-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4≤L≤16. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.52(7) and 1.25(11) using 6≤L≤12, respectively, which are in very good agreement with the Monte Carlo results and with the theoretical predictions of 5/2 and 5/4. The critical temperature for the infinite lattice is found to be 8.779(8) using 8≤L≤16 which is also in very good agreement with the recent precise results.
The five-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using finite-size lattices with the linear dimensions L = 4, 6, 8, 10, 12, 14, and 16. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically-predicted expression near the infinite-lattice critical temperature. The approximate values for the critical temperature of the infinite-lattice, Tc = 8.8063, Tc = 8.7825 and Tc = 8.7572, are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of Tc = 8.7787. The value obtained for the critical exponent of the specific heat, i.e. α = 0.009, is also in agreement with α = 0 predicted by the theory.
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