Crossover phenomena involving the dense O(nn) phase

We explore the properties of the low-temperature phase of the O($n$) loop model in two dimensions by means of transfer-matrix calculations and finite-size scaling. We determine the stability of this phase with respect to several kinds of perturbations, including cubic anisotropy, attraction between loop segments, double bonds and crossing bonds. In line with Coulomb gas predictions, cubic anisotropy and crossing bonds are found to be relevant and introduce crossover to different types of behavior. Whereas perturbations in the form of loop-loop attractions and double bonds are irrelevant, sufficiently strong perturbations of these types induce a phase transition of the Ising type, at least in the cases investigated. This Ising transition leaves the underlying universal low-temperature O($n$) behavior unaffected.Comment: 12 pages, 8 figure

Managing markets and money : issues and institutions in Dutch nineteenth-century economics

Dutch nineteenth-century economics was more modern than conventional scholarship has suggested. In a number of studies of individual economists and of the formal aspects of academia, it has been concluded that at least before 1870 there were no original contributions by Dutch economists and there was a general academic backwardness of the discipline. Here we try to examine simultaneously the issues of the day and the institutional setting of academic and political economic discourse. We concentrate upon the discussion of markets, in particular the question of free trade, and the discussion of money, in particular the problems of regulating the national debt and the currency. Our picture will be that in the new Kingdom of the Netherlands economics was embraced as the science of modernity, that very soon many courses of the subject were taught in the law faculties, and that a considerable number of university professors engaged in practical policy issues. In our opinion, there is more continuity in the economic thought of Van Hogendorp (who never held a university chair) and of Ackersdijck, Mees and Pierson than most historians of Dutch economics have perceived. The fact that the latter two have also been presidents of the central bank is significant for the importance of this institution in the history of Dutch economics. We conclude that in the first two decades of the century, the new discipline gained ground outside and inside academia. From around 1820 it was well established as a subject in the law faculties, and professors like Tydeman and Ackersdijck were seen as respected authorities in the public debate on economic issues. The year 1848 saw the acceptance of a new liberal constitution and the take-off of economics as an organised community with its own specific role in Dutch society.

Phase Diagram of a Loop on the Square Lattice

The phase diagram of the O(n) model, in particular the special case $n=0$, is studied by means of transfer-matrix calculations on the loop representation of the O(n) model. The model is defined on the square lattice; the loops are allowed to collide at the lattice vertices, but not to intersect. The loop model contains three variable parameters that determine the loop density or temperature, the energy of a bend in a loop, and the interaction energy of colliding loop segments. A finite-size analysis of the transfer-matrix results yields the phase diagram in a special plane of the parameter space. These results confirm the existence of a multicritical point and an Ising-like critical line in the low-temperature O(n) phase.Comment: LaTeX, 3 eps file

Crossover scaling in two dimensions

We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the reduced temperature as well as in the finite-size crossover variable, it has up to now largely evaded a satisfactory numerical determination. Using a new Monte Carlo method, we could obtain accurate results for sufficiently large interactions ranges. Our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal. Also the so-called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region.Comment: 24 pages RevTeX 3.0/3.1, including 22 PostScript figures. Uses epsf.st