Antiferromagnetic gap in the Hubbard model

We compute the temperature dependence of the antiferromagnetic order parameter and the gap in the two dimensional Hubbard model at and close to half filling. Our approach is based on truncations of an exact functional renormalization group equation. The explicit use of composite bosonic degrees of freedom permits a direct investigation of the ordered low temperature phase. We show that the Mermin--Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state. The critical behavior is dominated by the fluctuations of composite Goldstone bosons.Comment: new discussion of critical behavior 4 pages,2 figures, LaTe

Temperature dependence of antiferromagnetic order in the Hubbard model

We suggest a method for an approximative solution of the two dimensional Hubbard model close to half filling. It is based on partial bosonisation, supplemented by an investigation of the functional renormalisation group flow. The inclusion of both the fermionic and bosonic fluctuations leads in lowest order to agreement with the Hartree-Fock result or Schwinger-Dyson equation and cures the ambiguity of mean field theory . We compute the temperature dependence of the antiferromagnetic order parameter and the gap below the critical temperature. We argue that the Mermin-Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state of the Hubbard model. The long distance behavior close to and below the critical temperature is governed by the renormalisation flow for the effective interactions of composite Goldstone bosons and deviates strongly from the Hartree-Fock result.Comment: New section on critical behavior 31 pages,17 figure

Spontaneous symmetry breaking in the colored Hubbard model

The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of translationally invariant expectation values for colored composite scalar fields. A suitable mean field approximation for the two dimensional colored Hubbard model shows indeed phases with antiferromagnetic ordering or d-wave superconductivity at low temperature. At low enough temperature the transition to the antiferromagnetic phase is of first order. The present formulation also allows an easy extension to more complicated microscopic interactions.Comment: 19 pages, 5 figure

Diagrammatik der Architektur

Ist das ›unruhige Enzephalogramm‹, mit dem James Graham Ballard 1975 in seinem architekturkritischen Klassiker ›High Rise‹ die Silhouette von London gleichsetzt, schon gelesen worden? Oder selbstkritischer gefragt: Warum kann das Diagramm einen wesentlichen Aspekt zeitgenössischer Bildtheorie darstellen, während diese Kategorie im architektonischen Diskurs immer noch von den komplexen, letztlich aber instrumentell ausgerichteten Ansätzen der 1990er Jahre bestimmt wird? Auf einer Kölner Tagung im Januar 2011 wurde die Diagrammatik der Baukunst unter Berücksichtigung aktueller Ansätze der Bild- und Kulturtheorien neu bewertet. Die in diesem Band publizierten Beiträge aus unterschiedlichen Disziplinen – Architektur, Pädagogik, Kunstgeschichte, Informatik – zu Themenbereichen vom Mittelalter bis zur Gegenwart belegen, dass diagrammatische Darstellungen und Denkmuster in allen Bereichen der Architektur wichtig werden können, sei es für Lehre, Entwurf, Ausführung, Vermittlung oder Analyse. Ihre Fähigkeit, Momente der Operationalität, der Evidenz und der Spur zu vereinen, lassen sie zu einer Gelenkstelle zwischen verschiedenen zeitlichen und räumlichen Manifestationen von Architektur und ihren Medien werden

Flow Equations without Mean Field Ambiguity

We compare different methods used for non-perturbative calculations in strongly interacting fermionic systems. Mean field theory often shows a basic ambiguity related to the possibility to perform Fierz transformations. The results may then depend strongly on an unphysical parameter which reflects the choice of the mean field, thus limiting the reliability. This ambiguity is absent for Schwinger-Dyson equations or fermionic renormalization group equations. Also renormalization group equations in a partially bosonized setting can overcome the Fierz ambiguity if the truncation is chosen appropriately. This is reassuring since the partially bosonized renormalization group approach constitutes a very promising basis for the explicit treatment of condensates and spontaneous symmetry breaking even for situations where the bosonic correlation length is large.Comment: New version to match the one published in PRD. New title (former title: Solving Mean Field Ambiguity by Flow Equations), added section IX and appendix B. More explanations in the introduction and conclusions. 16 pages, 6 figures and 3 tables uses revtex

Towards a standardization of biomethane potential tests

Production of biogas from different organic materials is a most interesting source of renewable energy. The biomethane potential (BMP) of these materials has to be determined to get insight in design parameters for anaerobic digesters. Although several norms and guidelines for BMP tests exist, inter-laboratory tests regularly show high variability of BMPs for the same substrate. A workshop was held in June 2015, in Leysin, Switzerland, with over 40 attendees from 30 laboratories around the world, to agree on common solutions to the conundrum of inconsistent BMP test results. This paper presents the consensus of the intense roundtable discussions and cross-comparison of methodologies used in respective laboratories. Compulsory elements for the validation of BMP results were defined. They include the minimal number of replicates, the request to carry out blank and positive control assays, a criterion for the test duration, details on BMP calculation, and last but not least criteria for rejection of the BMP tests. Finally, recommendations on items that strongly influence the outcome of BMP tests such as inoculum characteristics, substrate preparation, test setup, and data analysis are presented to increase the probability of obtaining validated and reproducible results.info:eu-repo/semantics/publishedVersio