Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagom\'e lattice.Comment: 33 pages, Latex, 9 encapsulated postscript figures, J. Phys. A, in pres

No Exit? Withdrawal Rights and the Law of Corporate Reorganizations

Bankruptcy scholarship is largely a debate about the comparative merits of a mandatory regime on one hand and bankruptcy by free design on the other. By the standard account, the current law of corporate reorganization is mandatory. Various rules that cannot be avoided ensure that investors’ actions are limited and they do not exercise their rights against specialized assets in a way that destroys the value of a business as a whole. These rules solve collective action problems and reduce the risk of bargaining failure. But there are costs to a mandatory regime. In particular, investors cannot design their rights to achieve optimal monitoring as they could in a system of bankruptcy by free design. This Article suggests that the academic debate has missed a fundamental feature of the law. Bankruptcy operates on legal entities, not on firms in the economic sense. For this reason, sophisticated investors do not face a mandatory regime at all. The ability of investors to place assets in separate entities gives them the ability to create specific withdrawal rights in the event the firm encounters financial distress. There is nothing mandatory about rules like the automatic stay when assets can be partitioned off into legal entities that are beyond the reach of the bankruptcy judge. Thus, by partitioning assets of one economic enterprise into different legal entities, investors can create a tailored bankruptcy regime. In this way, legal entities serve as building blocks that can be combined to create specific and varied but transparent investor withdrawal rights. This regime of tailored bankruptcy has been unrecognized and underappreciated and may be preferable to both mandatory and free design regimes. By allowing a limited number of investors to opt out of bankruptcy in a particular, discrete, and visible way, investors as a group may be able to both limit the risk of bargaining failure and at the same time enjoy the disciplining effect that a withdrawal right brings with it