Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals

We prove a general rigorous lower bound for $W(\Lambda,q)=\exp(S_0(\Lambda,q)/k_B)$, the exponent of the ground state entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean lattice $\Lambda$. We calculate large-$q$ series expansions for the exact $W_r(\Lambda,q)=q^{-1}W(\Lambda,q)$ and compare these with our lower bounds on this function on the various Archimedean lattices. It is shown that the lower bounds coincide with a number of terms in the large-$q$ expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions $W_r(\Lambda,q)$ for large $q$ on the various lattices $\Lambda$. Plots of $W_r(\Lambda,q)$ are given, and the general dependence on lattice coordination number is noted. Lower bounds and series are also presented for the duals of Archimedean lattices. As part of the study, the chromatic number is determined for all Archimedean lattices and their duals. Finally, we report calculations of chromatic zeros for several lattices; these provide further support for our earlier conjecture that a sufficient condition for $W_r(\Lambda,q)$ to be analytic at $1/q=0$ is that $\Lambda$ is a regular lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in Phys. Rev.

New polymorph of InVO4: A high-pressure structure with six-coordinated vanadium

This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Inorganic Chemestry, copyright © American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/ic402043xA new wolframite-type polymorph of InVO4 is identified under compression near 7 GPa by in situ high-pressure (HP) X-ray diffraction (XRD) and Raman spectroscopic investigations on the stable orthorhombic InVO4. The structural transition is accompanied by a large volume collapse (Delta V/V = -14%) and a drastic increase in bulk modulus (from 69 to 168 GPa). Both techniques also show the existence of a third phase coexisting with the low- and high-pressure phases in a limited pressure range close to the transition pressure. XRD studies revealed a highly anisotropic compression in orthorhombic InVO4. In addition, the compressibility becomes nonlinear in the HP polymorph. The volume collapse in the lattice is related to an increase of the polyhedral coordination around the vanadium atoms. The transformation is not fully reversible. The drastic change in the polyhedral arrangement observed at the transition is indicative of a reconstructive phase transformation. The HP phase here found is the only modification of InVO4 reported to date with 6-fold coordinated vanadium atoms. Finally, Raman frequencies and pressure coefficients in the low- and high-pressure phases of InVO4 are reported.This research supported by the Spanish government MINECO under Grant Nos. MAT2010-21270-C04-01/04 and CSD2007-00045. O.G. acknowledges support from Vicerrectorado de Investigacion y Desarrollo of UPV (Grant No. UPV2011-0914 PAID-05-11 and UPV2011-0966 PAID-06-11). S.N.A. acknowledges support provided by Universitat de Valencia during his visit to it. B.G.-D. acknowledges the financial support from MINECO through the FPI program.Errandonea, D.; Gomis Hilario, O.; García-Domene, B.; Pellicer Porres, J.; Katari, V.; Achary, SN.; Tyagi, AK.... (2013). New polymorph of InVO4: A high-pressure structure with six-coordinated vanadium. Inorganic Chemistry. 52(21):12790-12798. https://doi.org/10.1021/ic402043xS1279012798522