Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

Integrability vs non-integrability: Hard hexagons and hard squares compared

In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes $40\times40$ and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point $z=-1$ of hard squares where all eigenvalues have unit modulus, and we give several conjectures for the value at $z=-1$ of the partition functions.Comment: 46 page

The Anatomy of Grey: A Theory of Interracial Convergence

This article offers a theory of racial identity divorced from biological considerations. Law fails to recognize the complexity of racial performance and identity, thus categorically simplifying a perceived polarity of black and white. Ground-breaking scholarship addressing racial boundaries, as written by Randall Kennedy, Elizabeth Bartholet, and Angela Onwauchi-Willig, generally focuses on the enduring legacy of race discrimination. We approach these boundaries from a different angle—whites who become “less white.” We bring together the challenges of passing and adoption to offer a theory of fluid racial boundaries. Transracial adoption provides one viable channel to discuss the possibilities of white-to-black racial identity transformation. By confronting the meaning of white identity in relation to their black surroundings, adoptive parents may engage along a continuum of what we term “interracial convergence.” Parents who adopt transracially potentially face some of the pressures of being black in the United States. The Interethnic Placement Act forbids the consideration of race in adoption placements, but white adoptive parents nevertheless receive sharp criticism from black social workers for lacking the ability to teach “survival skills” necessary for the child’s racial identity development. We argue, alternatively, that it creates a grey space where racial convergers—adoptive parents and racial passers—can challenge the stability of racial boundaries

Deuterium on Venus: Observations from Earth

In view of the importance of the deuterium-to-hydrogen ratio in understanding the evolutionary scenario of planetary atmospheres and its relationship to understanding the evolution of our own Earth, we undertook a series of observations designed to resolve previous observational conflicts. We observed the dark side of Venus in the 2.3 micron spectral region in search of both H2O and HDO, which would provide us with the D/H ratio in Venus' atmosphere. We identified a large number of molecular lines in the region, belonging to both molecules, and, using synthetic spectral techniques, obtained mixing ratios of 34 plus or minus 10 ppm and 1.3 plus or minus 0.2 ppm for H2O and HDO, respectively. These mixing ratios yield a D/H ratio for Venus of D/H equals 1.9 plus or minus 0.6 times 10 (exp 12) and 120 plus or minus 40 times the telluric ratio. Although the detailed interpretation is difficult, our observations confirm that the Pioneer Venus Orbiter results and establish that indeed Venus had a period in its early history in which it was very wet, perhaps not unlike the early wet period that seems to have been present on Mars, and that, in contrast to Earth, lost much of its water over geologic time

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Processes of Change in Psychotherapy for Narcissistic Personality Disorder.

The present study aims at determining the role for outcome of potential processes of change in psychotherapy for narcissistic personality disorder (NPD). They were examined on three levels: the content, the process, and the relationship. A total of 161 patients suffering with NPD were recruited in a naturalistic setting as part of the present study. They underwent a long- term clarification-oriented psychotherapy. Sessions 15, 20, and 25 were video- or audio-recorded and analyzed with an observer-rated instrument that measures the quality of the interaction processes from the patient's and therapist's perspectives. Different self-report measures were used to assess therapy outcomes. In-session improvement was observed in both patient and therapist processes across sessions. Patient improvement in the three levels of processes was systematically related with outcome. Only partial relationships were found between therapist improvement and outcome. The present study represents the first systematic insight into core changes in patients with NPD undergoing psychotherapy

Modeling affirmative and negated action processing in the brain with lexical and compositional semantic models

Recent work shows that distributional semantic models can be used to decode patterns of brain activity associated with individual words and sentence meanings. However, it is yet unclear to what extent such models can be used to study and ecode fMRI patterns associated with specific aspects of semantic composition such as the negation function. In this paper, we apply lexical and compositional semantic models to decode fMRI patterns associated with negated and affirmative sentences containing hand-action verbs. Our results show reduced decoding (correlation) of sentences where the verb is in the negated context, as compared to the affirmative one, within brain regions implicated in action-semantic processing. This supports behavioral and brain imaging studies, suggesting that negation involves reduced access to aspects of the affirmative mental representation. The results pave the way for testing alternate semantic models of negation against human semantic processing in the brain