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.

H.M.'s personal crossword puzzles: understanding memory and language.

The amnesic patient H.M. has been solving crossword puzzles nearly all his life. Here, we analysed the linguistic content of 277 of H.M.'s crossword-puzzle solutions. H.M. did not have any unusual difficulties with the orthographic and grammatical components inherent to the puzzles. He exhibited few spelling errors, responded with appropriate parts of speech, and provided answers that were, at times, more convincing to observers than those supplied by the answer keys. These results suggest that H.M.'s lexical word-retrieval skills remain fluid despite his profound anterograde amnesia. Once acquired, the maintenance of written language comprehension and production does not seem to require intact medial temporal lobe structures.