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.

Internal languages of retrieval: the bilingual encoding of memories for the personal past.

In contrast to most research on bilingual memory that focuses on how words in either lexicon are mapped onto memory for objects and concepts, we focus on memory for events in the personal past. Using a word-cue technique in sessions devoted exclusively to one language, we found that older Hispanic immigrants who had come to the United States as adults internally retrieved autobiographical memories in Spanish for events in the country of origin and in English for events in the U.S. These participants were consistently capable of discerning whether a memory had come to them "in words" or not, reflecting the distinction between purely imagistic or conceptual memories and specifically linguistic memories. Via examination of other phenomenological features of these memories (sense of re-living, sensory detail, emotionality, and rehearsal), we conclude that the linguistic/nonlinguistic distinction is fundamental and independent of these other characteristics. Bilinguals encode and retrieve certain autobiographical memories in one or the other language according to the context of encoding, and these linguistic characteristics are stable properties of those memories over time.