Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model

We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale Lambda_{MF} in one-loop approximation, which captures in particular the generation of an attraction in the d-wave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity and triplet pi-pairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet pi-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.Comment: 28 pages, 14 figure

Sculplexity: Sculptures of Complexity using 3D printing

We show how to convert models of complex systems such as 2D cellular automata into a 3D printed object. Our method takes into account the limitations inherent to 3D printing processes and materials. Our approach automates the greater part of this task, bypassing the use of CAD software and the need for manual design. As a proof of concept, a physical object representing a modified forest fire model was successfully printed. Automated conversion methods similar to the ones developed here can be used to create objects for research, for demonstration and teaching, for outreach, or simply for aesthetic pleasure. As our outputs can be touched, they may be particularly useful for those with visual disabilities.Comment: Free access to article on European Physics Letter

Incentive Effects of Funding Contracts: An Experiment

We examine the incentive effects of funding contracts on entrepreneurial effort decisions and allocative efficiency. We experiment with four types of contracts (standard debt contract, outside equity, non-monotonic contract, full-subsidy contract) that differ in the structure of investor repayment and, therefore, in the incentives for entrepreneurial effort provision. Theoretically the replacement of a standard debt contract by a repayment-equivalent non-monotonic contract reduces effort distortions and increases efficiency. We test this non-monotonic-contracts hypothesis in the laboratory as well. Our results reveal that the incentive effects of funding contracts need to be experienced before they reect in observed behavior. With sufficient experience observed behavior is consistent with the theoretical predictions and supports the non-monotonic-contracts hypothesis: we find that the replacement of a standard debt contract by a repayment-neutral non-monotonic contract increases entrepreneurial income by 170% and total surplus by 30% in our setting.hidden information, funding contracts, incentives, experiment, standard debt contract, non-monotonic contract

<i>In Situ</i> Sampling of Relative Dust Devil Particle Loads and Their Vertical Grain Size Distributions

During a field campaign in the Sahara Desert in southern Morocco, spring 2012, we sampled the vertical grain size distribution of two active dust devils that exhibited different dimensions and intensities. With these in situ samples of grains in the vortices, it was possible to derive detailed vertical grain size distributions and measurements of the lifted relative particle load. Measurements of the two dust devils show that the majority of all lifted particles were only lifted within the first meter (~46.5% and ~61% of all particles; ~76.5 wt % and ~89 wt % of the relative particle load). Furthermore, ~69% and ~82% of all lifted sand grains occurred in the first meter of the dust devils, indicating the occurrence of ‘‘sand skirts.’’ Both sampled dust devils were relatively small (~15m and ~4–5m in diameter) compared to dust devils in surrounding regions; nevertheless, measurements show that ~58.5% to 73.5% of all lifted particles were small enough to go into suspension (<31 mm, depending on the used grain size classification). This relatively high amount represents only ~0.05 to 0.15 wt % of the lifted particle load. Larger dust devils probably entrain larger amounts of fine-grained material into the atmosphere, which can have an influence on the climate. Furthermore, our results indicate that the composition of the surface, on which the dust devils evolved, also had an influence on the particle load composition of the dust devil vortices. The internal particle load structure of both sampled dust devils was comparable related to their vertical grain size distribution and relative particle load, although both dust devils differed in their dimensions and intensities. A general trend of decreasing grain sizes with height was also detected

Fermionic functional renormalization group for first-order phase transitions: a mean-field model

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.Comment: 17 pages, 8 figures. v2 corrects typos, adds references and a discussion of the literatur

A fundamental measure theory for the sticky hard sphere fluid

We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of weighted densities and an exact result from scaled particle theory (SPT). It is demonstrated that the excess free energy density of the inhomogeneous SHS fluid $\Phi_{\text{SHS}}$ is uniquely defined when (a) it is solely a function of the weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A {\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c) it yields any given direct correlation function (DCF) from the class of generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J. Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very good agreement with simulation data. In particular, this FMT yields the correct contact value of the density profiles with no adjustable parameters. Rather than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT produces them. Interestingly, although equivalent to Kierlik and Rosinberg's FMT in the case of hard spheres, the set of weighted densities used for Rosenfeld's original FMT is insufficient for constructing a DFT which yields the SHS DCF.Comment: 11 pages, 3 figure

A pure variation of risk in private-value auctions

We introduce a new method of varying risk that bidders face in first-price and second-price private value auctions. We find that decreasing bidders’ risk in first-price auction reduces the degree of overbidding relative to the risk-neutral Bayesian Nash equilibrium prediction.This finding is consistent with the risk-aversion explanation of overbidding. Furthermore, we apply the method to second-price auctions and find that bidding behavior is robust to manipulating bidders'' risk as generally expected in auction theory.microeconomics ;

A pure variation of risk in first-price auctions

We introduce a new method of varying the risk that bidders face in first-price private value auctions. We find that decreasing bidders’ risk significantly reduces the degree of overbidding relative to the risk-neutral Bayesian-Nash equilibrium prediction. This implies that risk affects bidding behavior as generally expected in auction theory. While resolving a long-standing debate on the effect of risk on auction behavior, our results give rise to a new puzzle. As risk is diminished and overbidding decreases for most of the value range, a significant degree of underbidding sets in for very low valuesEconomics (Jel: A)

On the Birth of Isolas

Isolas are isolated, closed curves of solution branches of nonlinear problems. They have been observed to occur in the buckling of elastic shells, the equilibrium states of chemical reactors and other problems. In this paper we present a theory to describe analytically the structure of a class of isolas. Specifically, we consider isolas that shrink to a point as a parameter τ of the problem, approaches a critical value τ_0. The point is referred to as an isola center. Equations that characterize the isola centers are given. Then solutions are constructed in a neighborhood of the isola centers by perturbation expansions in a small parameter ε that is proportional to (τ-τo), with a appropriately determined. The theory is applied to a chemical reactor problem