scholarly journals Grassmann tensor renormalization group for the one-flavor lattice Gross–Neveu model with finite chemical potential

2015 ◽  
Vol 2015 (4) ◽  
Author(s):  
Shinji Takeda ◽  
Yusuke Yoshimura
Keyword(s):  
Renormalization Group ◽  
Chemical Potential ◽  
The One ◽  
Gross Neveu Model

Structure, Stability and Water Adsorption on Ultra-Thin TiO2 Supported on TiN

2019 ◽  
Author(s):  
Jose Julio Gutierrez Moreno ◽  
Marco Fronzi ◽  
Pierre Lovera ◽  
alan O'Riordan ◽  
Mike J Ford ◽  
...  
Keyword(s):  
Density Functional ◽  
Water Adsorption ◽  
Chemical Potential ◽  
Energy Gap ◽  
Molecular Water ◽  
Structure Stability ◽  
Ambient Conditions ◽  
Rutile Structure ◽  
The Stability ◽  
The One

<p></p><p>Interfacial metal-oxide systems with ultrathin oxide layers are of high interest for their use in catalysis. In this study, we present a density functional theory (DFT) investigation of the structure of ultrathin rutile layers (one and two TiO<sub>2</sub> layers) supported on TiN and the stability of water on these interfacial structures. The rutile layers are stabilized on the TiN surface through the formation of interfacial Ti–O bonds. Charge transfer from the TiN substrate leads to the formation of reduced Ti<sup>3+</sup> cations in TiO<sub>2.</sub> The structure of the one-layer oxide slab is strongly distorted at the interface, while the thicker TiO<sub>2</sub> layer preserves the rutile structure. The energy cost for the formation of a single O vacancy in the one-layer oxide slab is only 0.5 eV with respect to the ideal interface. For the two-layer oxide slab, the introduction of several vacancies in an already non-stoichiometric system becomes progressively more favourable, which indicates the stability of the highly non-stoichiometric interfaces. Isolated water molecules dissociate when adsorbed at the TiO<sub>2</sub> layers. At higher coverages the preference is for molecular water adsorption. Our ab initio thermodynamics calculations show the fully water covered stoichiometric models as the most stable structure at typical ambient conditions. Interfacial models with multiple vacancies are most stable at low (reducing) oxygen chemical potential values. A water monolayer adsorbs dissociatively on the highly distorted 2-layer TiO<sub>1.75</sub>-TiN interface, where the Ti<sup>3+</sup> states lying above the top of the valence band contribute to a significant reduction of the energy gap compared to the stoichiometric TiO<sub>2</sub>-TiN model. Our results provide a guide for the design of novel interfacial systems containing ultrathin TiO<sub>2</sub> with potential application as photocatalytic water splitting devices.</p><p></p>

Comparison of a Non Electrostatic Surface Complexation Model and Surface Phase Theories for Prediction of Future Sorption Properties.

2004 ◽  
Vol 824 ◽  
Author(s):  
Allan T. Emrén ◽  
Anna-Maria Jacobsson
Keyword(s):  
Aqueous Solution ◽  
Chemical Potential ◽  
Surface Complexation ◽  
Sorption Properties ◽  
Phase Method ◽  
Detailed Knowledge ◽  
Surface Phase ◽  
Surface Complexation Model ◽  
Advantages And Disadvantages ◽  
The One

AbstractIn performance assessments, sorption of radionuclides dissolved in groundwater is mostly handled by the use of fixed Kd values. It has been well known that this approach is unsatisfying. Only during the last few years, however, tools have become available that make it possible to predict the actual Kd value in an aqueous solution that differs from the one in which the sorption properties were measured.One such approach is surface complexation (SC) that gives a detailed knowledge of the sorption properties. In SC, one tries to find what kinds of sorbed species are available on the surface and the thermodynamics for their formation from species in the bulk aqueous solution. Recently, a different approach, surface phase method (SP), has been developed. In SP, a thin layer including the surface is treated as a separate phase. In the bulk aqueous solution, the surface phase is treated as a virtual component, and from the chemical potential of this component, the sorption properties can be found.In the paper, we compare advantages and disadvantages of the two kinds of models. We also investigate the differences in predicted sorption properties of a number of radionuclides (Co, Np, Th and U). Furthermore, we discuss under which circumstances, one approach or the other is preferable.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

scholarly journals EFFECT OF A LOCALLY REPULSIVE INTERACTION ON s-WAVE SUPERCONDUCTORS

2010 ◽  
Vol 22 (03) ◽  
pp. 233-303 ◽  
Author(s):  
J.-B BRU ◽  
W. DE SIQUEIRA PEDRA
Keyword(s):  
Phase Transition ◽  
Chemical Potential ◽  
Large Deviation ◽  
Coulomb Repulsion ◽  
Meissner Effect ◽  
Repulsive Interaction ◽  
S Wave ◽  
Insulator Phase Transition ◽  
The One ◽  
Strong Repulsion

The thermodynamic impact of the Coulomb repulsion on s-wave superconductors is analyzed via a rigorous study of equilibrium and ground states of the strong coupling BCS-Hubbard Hamiltonian. We show that the one-site electron repulsion can favor superconductivity at fixed chemical potential by increasing the critical temperature and/or the Cooper pair condensate density. If the one-site repulsion is not too large, a first or a second order superconducting phase transition can appear at low temperatures. The Meißner effect is shown to be rather generic but coexistence of superconducting and ferromagnetic phases is also shown to be feasible, for instance, near half-filling and at strong repulsion. Our proof of a superconductor-Mott insulator phase transition implies a rigorous explanation of the necessity of doping insulators to create superconductors. These mathematical results are consequences of "quantum large deviation" arguments combined with an adaptation of the proof of Størmer's theorem [1] to even states on the CAR algebra.

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

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