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.

Mechanical defenses in leaves eaten by Costa Rican howling monkeys (Alouatta palliata).

Primate species often eat foods of different physical properties. This may have implications for tooth structure and wear in those species. The purpose of this study was to examine the mechanical defenses of leaves eaten by Alouatta palliata from different social groups at Hacienda La Pacifica in Costa Rica. Leaves were sampled from the home-ranges of groups living in different microhabitats. Specimens were collected during the wet and dry seasons from the same tree, same plant part, and same degree of development as those eaten by the monkeys. The toughness of over 300 leaves was estimated using a scissors test on a Darvell mechanical tester. Toughness values were compared between social groups, seasons, and locations on the leaves using ANOVA. Representative samples of leaves were also sun-dried for subsequent scanning electron microscopy and energy dispersive x-ray (EDX) analyses in an attempt to locate silica on the leaves. Both forms of mechanical defense (toughness and silica) were found to be at work in the plants at La Pacifica. Fracture toughness varied significantly by location within single leaves, indicating that measures of fracture toughness must be standardized by location on food items. Monkeys made some food choices based on fracture toughness by avoiding the toughest parts of leaves and consuming the least tough portions. Intergroup and seasonal differences in the toughness of foods suggest that subtle differences in resource availability can have a significant impact on diet and feeding in Alouatta palliata. Intergroup differences in the incidence of silica on leaves raise the possibility of matching differences in the rates and patterns of tooth wear.