Exponential Control of Overlap in the Replica Method for <Emphasis Type="Italic">p</Emphasis>-Spin Sherrington-Kirkpatrick Model

In Talagrand (J. Stat. Phys. 126(4–5):837–894, 2007) the large deviations limit for the moments of the partition function Z _N in the Sherrington-Kirkpatrick model (Sherrington and Kirkpatrick in Phys. Rev. Lett. 35:1792–1796, 1972) was computed for all real a≥0. For a≥1 this result extends the classical physicist’s replica method that corresponds to integer values of a. We give a new proof for a≥1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap. This work is partially supported by NSF grant.     

Dynamics of α-Tocopherol Acetate: Proton Relaxation Studies Supported by Molecular Dynamics Simulations

Dynamical properties of α-tocopherol acetate (commonly known as vitamin E) have been investigated in a broad temperature range (below and above the glass transition) by means of proton spin–lattice relaxation. Two distinct relaxation processes have been detected in the studied temperature range. One of them, present in the solid phase, has been attributed to reorientation of methyl groups. In order to identify the motional process leading to the proton relaxation above the glass transition temperature (T _g), molecular dynamics (MD) simulations have been performed, which provided time correlation functions for several internuclear vectors in the molecule. The high-temperature relaxation process is primarily due to dynamics of the aromatic rings of the tocopherol molecule; however, a considerable contribution of diffusion of the aliphatic chain cannot be excluded. Comparing the nuclear magnetic resonance (NMR) results with MD and relaxation data of dielectric spectroscopy (DS) available in the literature (K. Kamiński, S. Maślanka, J. Zioło, M. Paluch, K.J. McGrath, C.M. Roland, Phys Rev E 75:011903-7, 2007; E. Szwajczak, J. Świergiel, R. Stagraczyński, J. Jadżyn, Phys Chem Liq 47:460–466, 2009), the motional process observed in NMR relaxation studies above T _g has been identified with the δ process observed in DS.     

On Convergence to SLE<Subscript>6</Subscript> I: Conformal Invariance for Certain Models of the Bond-Triangular Type

We show how to extract Cardy’s Formula for a general class of domains given the requisite interior analyticity statement. This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math. Phys. 19:511–565, 2007).     

On ‘light’ fermions and proton stability in ‘big divisor’ D3/D7 large volume compactifications

Building on our earlier work (Misra and Shukla, Nucl. Phys. B 827:112, 2010; Phys. Lett. B 685:347–352, 2010), we show the possibility of generating “light” fermion mass scales of MeV–GeV range (possibly related to the first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-brane restricted to (in principle) stacks of fluxed D7-branes wrapping the “big” divisor Σ _B . This part of the paper is an expanded version of the latter half of Sect. 3 of a published short invited review (Misra, Mod. Phys. Lett. A 26:1, 2011) written by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, and we estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10⁶¹ years. Based on GLSM calculations in (Misra and Shukla, Nucl. Phys. B 827:112, 2010) for obtaining the geometric K?hler potential for the “big divisor,” using further the Donaldson’s algorithm, we also briefly discuss in the first of the two appendices the metric for the Swiss-Cheese Calabi–Yau used, which we obtain and which becomes Ricci flat in the large-volume limit.     

Sufficient and Necessary Conditions of Entanglement Transformations Between Mixed States

Based on a new measure of entanglement for finite-dimensional bi-particle pure states, we give sufficient and necessary conditions that a bi-particle mixed state ρ can be transformed into another mixed state σ by local operations and classical communication (LOCC). This result can be regarded as a generalization of Nielsen’s theorem (Nielsen, Phys. Rev. Lett. 83:436, 1999). However, we find that it is more difficult to determine the entanglement transformations between mixed states than to do between pure ones.     

A new lattice measurement for potentials between static SU(3) sources

In this article, a new calculation of the static potentials between sources of different representations in SU(3) gauge group is presented. The results of the author’s previous study [Phys. Rev. D 62, 034509 (2000)] at the smallest lattice spacing a_s≃0.11 fm are shown to have been affected by finite volume effects. Within statistical errors, the new results obtained here are still in agreement with both Casimir scaling and flux tube counting. There is also no contradiction to the results obtained by Bali [Phys. Rev. D 62, 114503 (2000)] which however exclude flux counting. PACS 11.15.Ha; 12.38.Aw; 12.39.Pn; 12.38.Gc     

Non-uniqueness Results for Critical Metrics of Regularized Determinants in Four Dimensions

The regularized determinant of the Paneitz operator arises in quantum gravity [see Connes in (Noncommutative geometry, 1994), IV.4.γ]. An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in (Commun Math Phys 178:301–309, 1996). A similar formula holds for Cheeger’s half-torsion, which plays a role in self-dual field theory [see Juhl in (Families of conformally covariant differential operators, q-curvature and holography. Progress in Mathematics, vol 275, 2009)], and is defined in terms of regularized determinants of the Hodge laplacian on p-forms (p < n/2). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in (Commun Math Phys 149:241–262, 1992), (Ann Math 142:171–212, 1995), (Commun Math Phys 189:655–665, 1997).