Dynamic linear response of the SK spin glass coupled microscopically to a bath

The dynamic linear response theory of a general Ising model weakly coupled to a heat bath is derived employing the quantum statistical theory of Mori, treating the Hamiltonian of the spin bath coupling as a perturbation, and applying the Markovian approximation. Both the dynamic susceptibility and the relaxation function are expressed in terms of the static susceptibility and the static internal field distribution function. For the special case of the SK spin glass this internal field distribution can be related to the solutions of the TAP equations in the entire temperature region. Application of this new relation and the use of numerical solutions of the modified TAP equations leads for finite but large systems to explicit results for the distribution function and for dynamic linear response functions. A detailed discussion is presented which includes finite size effects. Due to the derived temperature dependence of the Onsager-Casimir coefficients a frequency-dependent shift of the cusp temperature of the real part of the dynamic susceptibility is found.Comment: 15 pages, 4 figures, submitted to J.Phys.A: Math. Ge

Consistent Conformal Extensions of the Standard Model

The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework for the study of the effective potential of the resulting multi-scalar standard model extensions. This approach relies on the assumption of the ordinary loop hierarchy $\lambda_\text{s} \sim g^2_\text{g}$ of scalar and gauge couplings. On the other hand, Andreassen, Frost and Schwartz recently argued that in the (single-scalar) standard model, gauge invariant results require the consistent scaling $\lambda_\text{s} \sim g^4_\text{g}$. In the present paper we contrast these two hierarchy assumptions and illustrate the differences in the phenomenological predictions of minimal conformal extensions of the standard model.Comment: 20 pages, 19 figures. v2: Typo in (3.3) corrected, references adde

Hidden Conformal Symmetry in Tree-Level Graviton Scattering

We argue that the scattering of gravitons in ordinary Einstein gravity possesses a hidden conformal symmetry at tree level in any number of dimensions. The presence of this conformal symmetry is indicated by the dilaton soft theorem in string theory, and it is reminiscent of the conformal invariance of gluon tree-level amplitudes in four dimensions. To motivate the underlying prescription, we demonstrate that formulating the conformal symmetry of gluon amplitudes in terms of momenta and polarization vectors requires manifest reversal and cyclic symmetry. Similarly, our formulation of the conformal symmetry of graviton amplitudes relies on a manifestly permutation symmetric form of the amplitude function.Comment: 35 pages, 3 figure