Correlation Functions in Two-Dimensional Dilaton Gravity

The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$ case (i.e., without matter), the cosmological term operator is found to have the discrete momentum that plays a special role in the $c=1$ Liouville gravity. The correlation functions for arbitrary numbers of operators are found in the $N=0$ case, and are nonvanishing only for specific ``chirality'' configurations.Comment: 14 pages, TIT/HEP-204, STUPP-92-13

Incommensurate-Commensurate Magnetic Phase Transition in SmRu2_{2}Al10_{10}

Magnetic properties of single crystalline SmRu$_{2}$Al$_{10}$ have been investigated by electrical resistivity, magnetic susceptibility, and specific heat. We have confirmed the successive magnetic phase transitions at $T_{\text{N}}=12.3$ K and $T_{\text{M}}=5.6$ K. Resonant x-ray diffraction has also been performed to study the magnetic structures. Below $T_{\text{N}}$, the Sm$^{3+}$ moments order in an incommensurate structure with $q_1=(0, 0.759, 0)$. The magnetic moments are oriented along the orthorhombic $b$ axis, which coincides with the magnetization easy axis in the paramagnetic phase. A very weak third harmonic peak is also observed at $q_3=(0, 0.278, 0)$. The transition at $T_{\text{M}}$ is a lock-in transition to the commensurate structure described by $q_1=(0, 0.75, 0)$. A well developed third harmonic peak is observed at $q_3=(0, 0.25, 0)$. From the discussion of the magnetic structure, we propose that the long-range RKKY interaction plays an important role, in addition to the strong nearest neighbor antiferromagnetic interaction.Comment: 11 pages, 12 figures, accepted in PR

Stable Existence of Phase IV inside Phase II under Pressure in Ce0.8_{0.8}La0.2_{0.2}B6_{6}

We investigate the pressure effect of the electrical resistivity and magnetization of Ce$_{0.8}$La$_{0.2}$B$_{6}$. The situation in which phase IV stably exists inside phase II at H=0 T could be realized by applying a pressure above $P\sim 1.1$ GPa. This originates from the fact that the stability of phase II under pressure is larger than those of phases IV and III. The results seem to be difficult to reproduce by taking the four interactions of $\Gamma_{\mathrm{5u}}$-type AFO, $O_{xy}$-type AFQ, $T_{xyz}$-type AFO, and AF exchange into account within a mean-field calculation framework.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn. 79 (2010) No.

The Integrity of Marriage

While the Supreme Court’s decision in Obergefell v. Hodges resolved a dispute about access to legal marriage, it also exposed a rift between the Justices about what rights, obligations, and social meanings marriage should entail. The majority opinion described marriage as a “unified whole” comprised of “essential attributes,” both legal and extralegal. The dissents, in contrast, were more skeptical about marriage’s inherent legal content. Justice Scalia, for instance, characterized marriage as a mere bundle of “civil consequences” attached to “whatever sexual attachments and living arrangements [the law] wishes.” This side debate has taken center stage in several recent disputes. In the years following Obergefell, courts, including the United States Supreme Court, have considered whether the First Amendment limits a state’s authority to require public accommodations to provide equal access to services related to a wedding celebration, whether the right to marry encompasses the right to be deemed a parent to a child born to one’s spouse, and whether states can withhold valuable employment benefits from married same-sex couples. And numerous state legislatures have considered proposals to get states “out of the marriage business.” All of these disputes ultimately question how the positive law of marriage should be constituted and whether marriage is indeed a unified or integrated whole. Some scholars have analyzed these questions from a historical or functional perspective. This Article starts from a different point. It accepts Obergefell’s invitation to think of marriage as an institution that can be more or less “unified” or “integrated.” Along these lines, it proposes a new framework for analyzing questions about the positive law of marriage: the continuum of integration and disintegration. This continuum has two interrelated dimensions. The first involves the rights and duties that the law imposes upon spouses. The second involves the uniformity of those legal rules across jurisdictions. Marriage becomes more integrated when rights and social norms mutually reinforce each other, and less integrated when rights and norms conflict. The package of rights and norms becomes more integrated when it is uniform across jurisdictions, and less integrated when jurisdictional differences prevent marriage from acquiring a singular meaning. This integration framework has two benefits. First, by focusing attention on the relationship between the functions, laws, and norms of marriage, the integration framework provides a methodology for assessing claims that changes to marriage laws are bringing about marriage’s disintegration, rendering visible whether and how disintegration occurs. Second, it identifies benefits and costs of integration, demonstrating the extent to which marriage relies on effectively communicating information about its content but noting the downsides of centralization and state control. This integration framework enables a more principled analysis of efforts targeted at reforming marriage laws and recognizing nonmarital relationships