Frustrated two dimensional quantum magnets

We overview physical effects of exchange frustration and quantum spin fluctuations in (quasi-) two dimensional (2D) quantum magnets ($S=1/2$) with square, rectangular and triangular structure. Our discussion is based on the $J_1$-$J_2$ type frustrated exchange model and its generalizations. These models are closely related and allow to tune between different phases, magnetically ordered as well as more exotic nonmagnetic quantum phases by changing only one or two control parameters. We survey ground state properties like magnetization, saturation fields, ordered moment and structure factor in the full phase diagram as obtained from numerical exact diagonalization computations and analytical linear spin wave theory. We also review finite temperature properties like susceptibility, specific heat and magnetocaloric effect using the finite temperature Lanczos method. This method is powerful to determine the exchange parameters and g-factors from experimental results. We focus mostly on the observable physical frustration effects in magnetic phases where plenty of quasi-2D material examples exist to identify the influence of quantum fluctuations on magnetism.Comment: 78 pages, 54 figure

Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange

We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $\chi$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to $N=28$ sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on $c_V(T)$ and $\chi(T)$. We show the variation of peak position and peak height of these quantities as function of control parameter $J_2/J_1$. We demonstrate that maximum peak positions and heights in N\'eel phase and spiral phases are strongly asymmetric, much more than in the square lattice $J_1$-$J_2$ model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs$_2$CuCl$_4$ and Cs$_{2}$CuBr$_{4}$ from our FTLM results.Comment: 13 pages, 12 figure

An Investigation of the Factor Structure of the HARVARD GROUP SCALE OF HYPNOTIC SUSCEPTIBILITY, Form A (HGSHS:A)

In order to investigate the effects of the hypnotic state a standardized hypnosis session was conducted with 144 subjects in a controlled laboratory study. The induction of a hypnotic trance in the German version of the Harvard Group Scale of Hypnotic Susceptibility (HGSHS:A by Shor and Orne, 1962) was tape-recorded and used as the treatment. The HGSHS:A seems to be a reliable measure of suggestibility and hypnotizability. This is underlined by the consistent results of a factor analysis on the depths of hypnosis that is in agreement with former studies. Descriptive data analyses with a sufficient number of subjects of high and low suggestibility suggest that our hypnosis induction by tape is an effective method of producing a hypnotic trance. Analyses of within-subjects variables did not reveal any valid predictors of hypnotizability, thereby confirming the need of screening instruments such as the HGSHS

N\'eel temperature and reentrant H-T phase diagram of quasi-2D frustrated magnets

In quasi-2D quantum magnets the ratio of N\'eel temperature $T_\text N$ to Curie-Weiss temperature $\Theta_\text{CW}$ is frequently used as an empirical criterion to judge the strength of frustration. In this work we investigate how these quantities are related in the canonical quasi-2D frustrated square or triangular $J_1$-$J_2$ model. Using the self-consistent Tyablikov approach for calculating $T_\text N$ we show their dependence on the frustration control parameter $J_2/J_1$ in the whole N\'eel and columnar antiferromagnetic phase region. We also discuss approximate analytical results. In addition the field dependence of $T_\text N(H)$ and the associated possible reentrance behavior of the ordered moment due to quantum fluctuations is investigated. These results are directly applicable to a class of quasi-2D oxovanadate antiferromagnets. We give clear criteria to judge under which conditions the empirical frustration ratio $f=\Theta_\text{CW}/T_\text N$ may be used as measure of frustration strength in the quasi-2D quantum magnets.Comment: 16 pages, 14 figures, to appear in Physical Review

Quantum fluctuations in anisotropic triangular lattices with ferro- and antiferromagnetic exchange

The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. Motivated by recent experimental findings on Cs$_{2}$CuCl$_{4-x}$Br$_{x}$, we discuss the full phase diagram of the anisotropic model with two exchange constants $J_{1}$ and $J_{2}$, including possible ferromagnetic exchange. Furthermore a comparison with the related square lattice model is carried out. We discuss the zero-temperature phase diagram, ordering vector, ground-state energy, and ordered moment on a classical level and investigate the effect of quantum fluctuations within the framework of spin-wave theory. The field dependence of the ordered moment is shown to be nonmonotonic with field and control parameter.Comment: 13 pages, 14 figure

Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange

We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $\chi$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to $N=28$ sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on $c_V(T)$ and $\chi(T)$. We show the variation of peak position and peak height of these quantities as function of control parameter $J_2/J_1$. We demonstrate that maximum peak positions and heights in N\'eel phase and spiral phases are strongly asymmetric, much more than in the square lattice $J_1$-$J_2$ model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs$_2$CuCl$_4$ and Cs$_{2}$CuBr$_{4}$ from our FTLM results.Comment: 13 pages, 12 figure

[2.2](4,7)Isobenzofuranophanes - Synthesis, Characterisation and Reactivity

The isomeric Diels-Alder adducts 3, obtained by cycloaddition of tetraphenylcyclopentadienone to the 4,5:12,13-bis-(oxanorbornadieno)[2.2]paracyclophanes syn,syn- and anti,-syn-2[Note ][The stereochemical descriptors syn and anti refer to the orientation of the oxygen bridge in the oxabicyclo[2.2.1]heptadiene subunits with respect to the [2.2]paracyclophaneskeleton.], yield the unstable isobenzofuranophane 4 by consecutive extrusion of carbon monoxide and tetraphenylbenzene when heated to 180°C. The molecular ion of 4 was observed in the EI mass spectrum. The stable tetraphenyl-substituted analogue 10 was synthesized independently from the previously unknown 4,5,12,13-tetrabenzoyl[2.2]paracyclophane (9). UV/Vis as well as fluorescence spectra and an X-ray crystal structure analysis of 9 are reported

Third-order magnetic susceptibility of the frustrated square-lattice antiferromagnet

We present results from our analysis of the finite-temperature properties of the spin 1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice. The analysis is based on the exact diagonalization of small clusters with 16 and 20 sites utilizing the finite-temperature Lanczos method. In particular, we focus on the temperature dependence of the third-order magnetic susceptibility as a method to resolve the ambiguity of exchange constants. We discuss the entire range of the frustration angle $\phi=\tan^{-1}(J_{2}/J_{1})$ parameterizing the different possible phases of the model, including the large region in the phase diagram with at least one ferromagnetic exchange constant.Comment: 2 pages, 2 figure

Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies.Symmetric two-player games, zero-sum games, Rock-Paper-Scissors, single-peakedness, quasiconcavity, finite population evolutionary stable strategy, saddle point, exact potential games

Once Beaten, Never Again: Imitation in Two-Player Potential Games

We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.Imitate-the-best, learning, exact potential games, symmetric games, relative payoffs, zero-sum games