Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

How Locally Designed Access and Use Controls Can Prevent the Tragedy of the Commons in a Mexican Small-Scale Fishing Community

The Seri people, a self-governed community of small-scale fishermen in the Gulf of California, Mexico, have ownership rights to fishing grounds where they harvest highly valuable commercial species of bivalves. Outsiders are eager to gain access, and the community has devised a set of rules to allow them in. Because Seri government officials keep all the economic benefits generated from granting this access for themselves, community members create alternative entry mechanisms to divert those benefits to themselves. Under Hardin’s model of the tragedy of the commons, this situation would eventually lead to the overexploitation of the fishery. The Seri people, however, are able to simultaneously maintain access and use controls for the continuing sustainability of their fishing grounds. Using insights from common- pool resources theory, I discuss how Seri community characteristics help mediate the conflict between collective action dilemmas and access and use controls.