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.

The `Ulama' and the State: Negotiating Tradition, Authority and Sovereignty in Contemporary Pakistan

This dissertation is an account of how contemporary Pakistani ulama grapple with their political realities and the Islamic state of Pakistan. The central conceptual question that scaffolds my dissertation is: How do Pakistani ulama negotiate tradition, authority and sovereignty with the Islamic Republic of Pakistan? In engaging with this issue, this dissertation employs a methodology that weds ethnography with rigorous textual analysis. The ulama that feature in this study belong to a variety of sectarian persuasions. The Sunni ulama are Deobandi and Barelvi; the Shia ulama in this study are Ithna Ashari.

In assessing the relationship between Pakistani ulama and their nation-state, I assert that the ulama's dialectical engagements with the state are best understood as a dexterous navigation between affirmation, critique, contestation and cultivation. In proposing this manner of thinking about Pakistani ulama's engagements with their state, I provide a more detailed and nuanced view of the ulama-state relationship compared to earlier works. While emphasizing Pakistani ulama's vitality and their impact on their state, this dissertation also draws attention to the manners in which the state impacts the ulama. It theorizes the subject formation of the ulama and asserts the importance of understanding the ulama as formed not just by the ethico-legal tradition in which they are trained but also by the state apparatus.