Phase Transition in the Two Dimensional Classical XY Model

For the two dimensional classical XY model we present extensive high -temperature -phase bulk data extracted based on a novel finite size scaling (FSS) Monte Carlo technique, along with FSS data near criticality. Our data verify that $\eta=1/4$ sets in near criticality, and clarify the nature of correction to the leading scaling behavior. However, the result of standard FSS analysis near criticality is inconsistent with other predictions of Kosterlitz's renormalization group approach.Comment: Significant changes in the text and the figures. To appear in Phys. Lett. A Hard copies of seven figures are available upon reques

Ontology as Transcendental Philosophy

How does the critical Kant view ontology? There is no shared scholarly answer to this question. Norbert Hinske sees in the Critique of Pure Reason a “farewell to ontology,” albeit one that took Kant long to bid (Hinske 2009). Karl Ameriks has found evidence in Kant’s metaphysics lectures from the critical period that he “was unwilling to break away fully from traditional ontology” (Ameriks 1992: 272). Gualtiero Lorini argues that a decisive break with the tradition of ontology is essential to Kant’s critical reform of metaphysics, as is reflected in his shift from “ontology” to “transcendental philosophy,” two notions that Lorini takes to be related by mere “analogy” (Lorini 2015). I agree with Lorini that a thorough reform of ontology is a pivotal part of Kant’s critical plan for metaphysics and that ontology somehow “survives within the critical philosophy” (Lorini 2015: 76). To make this case, however, I deem it important to identify “ontology” and “transcendental philosophy” in the sense of extensional equivalence. While we can detect this identification in Kant’s writings, only from his metaphysics lectures can we get a full sense of its historical and philosophical significance. In this chapter I focus on how it represents a definitive turn from as well as notable continuity with traditional treatments of ontology, particularly the Wolffian one

A Guide to Ground in Kant's Lectures on Metaphysics

While scholars have extensively discussed Kant’s treatment of the Principle of Sufficient Ground in the Antinomies chapter of the Critique of Pure Reason, and, more recently, his relation to German rationalist debates about it, relatively little has been said about the exact notion of ground that figures in the PSG. My aim in this chapter is to explain Kant’s discussion of ground in the lectures and to relate it, where appropriate, to his published discussions of ground

The two-phase issue in the O(n) non-linear σ\sigma-model: A Monte Carlo study

We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.Comment: 3 pgs. espcrc2.sty included. Talk presented at LATTICE96(other models

On Your Mark, Get Set, Self-Control, Go: A Differentiated View on the Cortical Hemodynamics of Self-Control during Sprint Start

Most sports are self-control demanding. For example, during a sprint start, athletes have to respond as fast as possible to the start signal (action initiation) while suppressing the urge to start too early (action inhibition). Here, we examined the cortical hemodynamic response to these demands by measuring activity in the two lateral prefrontal cortices (lPFC), a central area for self-control processes. We analyzed activity within subregions of the lPFC, while subjects performed a sprint start, and we assessed if activation varied as a function of hemisphere and gender. In a counterbalanced within-subject design, 39 participants (age: mean (M) = 22.44, standard deviation (SD) = 5.28, 22 women) completed four sprint start conditions (blocks). In each block, participants focused on inhibition (avoid false start), initiation (start fast), no start (do not start) and a combined condition (start fast; avoid false start). We show that oxyhemoglobin in the lPFC increased after the set signal and this increase did not differ between experimental conditions. Increased activation was primarily observed in ventral areas of the lPFC, but only in males, and this increase did not vary between hemispheres. This study provides further support for the involvement of the ventral lPFC during a sprint start, while highlighting gender differences in the processing of sprint start-induced self-control demands

Anisotropic Dirac fermions in a Bi square net of SrMnBi2

We report the highly anisotropic Dirac fermions in a Bi square net of SrMnBi2, based on a first principle calculation, angle resolved photoemission spectroscopy, and quantum oscillations for high-quality single crystals. We found that the Dirac dispersion is generally induced in the (SrBi)+ layer containing a double-sized Bi square net. In contrast to the commonly observed isotropic Dirac cone, the Dirac cone in SrMnBi2 is highly anisotropic with a large momentum-dependent disparity of Fermi velocities of ~ 8. These findings demonstrate that a Bi square net, a common building block of various layered pnictides, provide a new platform that hosts highly anisotropic Dirac fermions.Comment: 5 pages, 4 figure

Perturbation theory predictions and Monte Carlo simulations for the 2-d O(n) non-linear sigma-model

By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough lattices to have a good control on finite-size effects. The magnetic susceptibility and three different definitions of the correlation length are measured. We check our results with large-n expansions as well as with standard formulae for asymptotic freedom up to 4 loops in the standard and effective schemes. For this purpose the weak coupling expansions of the energy up to 4 loops for the standard action and up to 3 loops for the Symanzik action are calculated. For the O(3) model we have used two different effective schemes and checked that they lead to compatible results. A great improvement in the results is obtained by using the effective scheme based on the energy at 3 and 4 loops. We find that the O(8) model follows very nicely (within few per mille) the perturbative predictions. For the O(3) model an acceptable agreement (within few per cent) is found.Comment: latex source + 15 e-postscript figures. It generates 26 pgs. Replaced version containing more corrections to scaling for the Symanzik action, more detailed explanation of the calculation of $C_\chi$ and a few more citation