Complex-Temperature Singularities of Ising Models

We report new results on complex-temperature properties of Ising models. These include studies of the $s=1/2$ model on triangular, honeycomb, kagom\'e, $3 \cdot 12^2$, and $4 \cdot 8^2$ lattices. We elucidate the complex--$T$ phase diagrams of the higher-spin 2D Ising models, using calculations of partition function zeros. Finally, we investigate the 2D Ising model in an external magnetic field, mapping the complex--$T$ phase diagram and exploring various singularities therein. For the case $\beta H=i\pi/2$, we give exact results on the phase diagram and obtain susceptibility exponents $\gamma'$ at various singularities from low-temperature series analyses.Comment: 4 pages, latex, to appear in the Proceedings of Lattice-9

Extreme sensitivity of a frustrated quantum magnet: Cs_2CuCl_4

We report a thorough theoretical study of the low temperature phase diagram of Cs_2CuCl_4, a spatially anisotropic spin S=1/2 triangular lattice antiferromagnet, in a magnetic field. Our results, obtained in a quasi-one-dimensional limit in which the system is regarded as a set of weakly coupled Heisenberg chains, are in excellent agreement with experiment. The analysis reveals some surprising physics. First, we find that, when the magnetic field is oriented within the triangular layer, spins are actually most strongly correlated within planes perpendicular to the triangular layers. This is despite the fact that the inter-layer exchange coupling in Cs_2CuCl_4 is about an order of magnitude smaller than the weakest (diagonal) exchange in the triangular planes themselves. Second, the phase diagram in such orientations is exquisitely sensitive to tiny interactions, heretofore neglected, of order a few percent or less of the largest exchange couplings. These interactions, which we describe in detail, induce entirely new phases, and a novel commensurate-incommensurate transition, the signatures of which are identified in NMR experiments. We discuss the differences between the behavior of Cs_2CuCl_4 and an ideal two-dimensional triangular model, and in particular the occurrence of magnetization plateaux in the latter. These and other related results are presented here along with a thorough exposition of the theoretical methods, and a discussion of broader experimental consequences to Cs_2CuCl_4 and other materials.Comment: 43 pages, 20 figures; typos correcte

Phase transition of zircon at high P-T conditions

In situ observations of the zircon-reidite transition in ZrSiO4 were carried out using a multianvil high-pressure apparatus and synchrotron radiation. The phase boundary between zircon and reidite was determined to be P (GPa) = 8.5 + 0.0017×(T-1200) (K) for temperatures between 1100-1900 K. When subducted slabs, including igneous rocks and sediments, descend into the upper mantle, zircon in the subducted slab transforms into reidite at pressures of about 9 GPa, corresponding to a depth of 270 km. Reidite found in an upper Eocene impact ejecta layer in marine sediments is thought to have been transformed from zircon by a shock event. The peak pressure generated by the shock event in this occurrence is estimated to be higher than 8 GPa

Complex-Temperature Phase Diagram of the 1D Z6Z_6 Clock Model and its Connection with Higher-Dimensional Models

We determine the exact complex-temperature (CT) phase diagram of the 1D $Z_6$ clock model. This is of interest because it is the first exactly solved system with a CT phase boundary exhibiting a finite-$K$ intersection point where an odd number of curves (namely, three) meet, and yields a deeper insight into this phenomenon. Such intersection points occur in the 3D spin 1/2 Ising model and appear to occur in the 2D spin 1 Ising model. Further, extending our earlier work on the higher-spin Ising model, we point out an intriguing connection between the CT phase diagrams for the 1D and 2D $Z_6$ clock models.Comment: 10 pages, latex, with two epsf figure

Zeros of the Partition Function for Higher--Spin 2D Ising Models

We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the thermodynamic limit. Support is adduced for a conjecture that all divergences of the magnetisation occur at endpoints of arcs of zeros protruding into the FM phase. We conjecture that there are $4[s^2]-2$ such arcs for $s \ge 1$, where $[x]$ denotes the integral part of $x$.Comment: 8 pages, latex, 3 uuencoded figure

In Vivo Function and Evolution of the Eutherian-Specific Pluripotency Marker UTF1

Embryogenesis in placental mammals is sustained by exquisite interplay between the embryo proper and placenta. UTF1 is a developmentally regulated gene expressed in both cell lineages. Here, we analyzed the consequence of loss of the UTF1 gene during mouse development. We found that homozygous UTF1 mutant newborn mice were significantly smaller than wild-type or heterozygous mutant mice, suggesting that placental insufficiency caused by the loss of UTF1 expression in extra-embryonic ectodermal cells at least in part contributed to this phenotype. We also found that the effects of loss of UTF1 expression in embryonic stem cells on their pluripotency were very subtle. Genome structure and sequence comparisons revealed that the UTF1 gene exists only in placental mammals. Our analyses of a family of genes with homology to UTF1 revealed a possible mechanism by which placental mammals have evolved the UTF1 genes.This study was supported in part by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), and mostly by the Support Program for the Strategic Research Foundation at Private Universities, 2008–2012. This study was performed as a part of the Core Research for Evolutional Science and Technology (CREST) Agency. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Complex-Temperature Singularities in the d=2d=2 Ising Model. III. Honeycomb Lattice

We study complex-temperature properties of the uniform and staggered susceptibilities $\chi$ and $\chi^{(a)}$ of the Ising model on the honeycomb lattice. From an analysis of low-temperature series expansions, we find evidence that $\chi$ and $\chi^{(a)}$ both have divergent singularities at the point $z=-1 \equiv z_{\ell}$ (where $z=e^{-2K}$), with exponents $\gamma_{\ell}'= \gamma_{\ell,a}'=5/2$. The critical amplitudes at this singularity are calculated. Using exact results, we extract the behaviour of the magnetisation $M$ and specific heat $C$ at complex-temperature singularities. We find that, in addition to its zero at the physical critical point, $M$ diverges at $z=-1$ with exponent $\beta_{\ell}=-1/4$, vanishes continuously at $z=\pm i$ with exponent $\beta_s=3/8$, and vanishes discontinuously elsewhere along the boundary of the complex-temperature ferromagnetic phase. $C$ diverges at $z=-1$ with exponent $\alpha_{\ell}'=2$ and at $v=\pm i/\sqrt{3}$ (where $v = \tanh K$) with exponent $\alpha_e=1$, and diverges logarithmically at $z=\pm i$. We find that the exponent relation $\alpha'+2\beta+\gamma'=2$ is violated at $z=-1$; the right-hand side is 4 rather than 2. The connections of these results with complex-temperature properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a compressed, uuencoded postscript fil