General Solutions of Braneworlds under the Schwarzschild Ansatz

General solutions for braneworld dynamics coupled with the bulk Einstein equation are derived under the Schwarzschild ansatz. They relate the brane metric to the exterior configurations, and establish fine tuning conditions for the braneworlds to reproduce successes of the Einstein gravity.Comment: 4 page

Effect of second-rank random anisotropy on critical phenomena of random field O(N) spin model in the large N limit

We study the critical behavior of a random field O($N$) spin model with a second-rank random anisotropy term in spatial dimensions $4<d<6$, by means of the replica method and the 1/N expansion. We obtain a replica-symmetric solution of the saddle-point equation, and we find the phase transition obeying dimensional reduction. We study the stability of the replica-symmetric saddle point against the fluctuation induced by the second-rank random anisotropy. We show that the eigenvalue of the Hessian at the replica-symmetric saddle point is strictly positive. Therefore, this saddle point is stable and the dimensional reduction holds in the 1/N expansion. To check the consistency with the functional renormalization group method, we obtain all fixed points of the renormalization group in the large $N$ limit and discuss their stability. We find that the analytic fixed point yielding the dimensional reduction is practically singly unstable in a coupling constant space of the given model with large $N$. Thus, we conclude that the dimensional reduction holds for sufficiently large $N$.Comment: 19 pages, 5 figure

Comment on ``Random-Field Spin Model beyond 1 Loop: A Mechanism for Decreasing the Lower Critical Dimension"

A comment on the Letter by Le Doussal and Wiese, Phys. Rev. Lett. 96, 197202 (2006).Comment: 1 page. Comment on cond-mat/0510344 (Phys. Rev. Lett. 96, 197202 (2006)). Reply to this comment is cond-mat/061231