Spin glasses in the non-extensive regime

Spin systems with long-range interactions are "non-extensive" if the strength of the interactions falls off sufficiently slowly with distance. It has been conjectured for ferromagnets, and more recently for spin glasses, that, everywhere in the non-extensive regime, the free energy is exactly equal to that for the infinite range model in which the characteristic strength of the interaction is independent of distance. In this paper we present the results of Monte Carlo simulations of the one-dimensional long-range spin glasses in the non-extensive regime. Using finite-size scaling, our results for the transition temperatures are consistent with this prediction. We also propose, and provide numerical evidence for, an analogous result for diluted long-range spin glasses in which the coordination number is finite, namely that the transition temperature throughout the non-extensive regime is equal to that of the infinite-range model known as the Viana-Bray model.Comment: 8 pages; corrected typos, additional background and references relating to FSS correction

Finite-size scaling above the upper critical dimension

We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of hyperscaling due to a dangerous irrelevant variable, applies only to k=0 fluctuations, and so there is only a single exponent eta describing power-law decay of correlations at criticality, in contrast to recent claims. With free boundary conditions the finite-size "shift" is greater than the rounding. Nonetheless, using T-T_L, where T_L is the finite-size pseudocritical temperature, rather than T-T_c, as the scaling variable, the data does collapse on to a scaling form which includes the behavior both at T_L, where the susceptibility chi diverges like L^{d/2} and at the bulk T_c where it diverges like L^2. These claims are supported by large-scale simulations on the 5-dimensional Ising model.Comment: 11 pages, 15 figure

Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and four space dimensions, and one-dimensional long-range models with diluted power-law interactions. We study three long-range models with different powers as follows: the first is approximately equivalent to a short-range model in three dimensions, the second to a short-range model in four dimensions, and the third to a short-range model in the mean-field regime. We study an observable proposed earlier by some of us which aims to distinguish the "replica symmetry breaking" picture of the spin-glass phase from the "droplet picture," finding that larger system sizes would be needed to unambiguously determine which of these pictures describes the low-temperature state of spin glasses best, except for the Sherrington-Kirkpatrick model which is unambiguously described by replica symmetry breaking. Finally, we also study the median integrated overlap probability distribution and a typical overlap distribution, finding that these observables are not particularly helpful in distinguishing the replica symmetry breaking and the droplet pictures.Comment: 11 pages, 6 figure

Finite-size critical scaling in Ising spin glasses in the mean-field regime

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.Comment: 10 pages, 7 figure

Empire of Culture: U.S. Entertainers and the Making of the Pacific Circuit, 1850-1890.

During the mid-nineteenth century, the ongoing development of a robust and expansive U.S. culture industry dovetailed with the emergence of a recognizable Pacific world shaped by the integrative forces of colonialism and capitalism. In the wake of the California Gold Rush, these seemingly disparate developments intersected as U.S. entertainers flocked to San Francisco and began to tour around the Pacific, giving birth to a vibrant entertainment circuit that fomented interactions and mediated exchanges between the United States and the diverse peoples and cultures of the Pacific world. This dissertation is a transnational cultural history of this Pacific circuit that focuses on the experiences of the U.S. entertainers that moved through it and their reciprocal interactions with the people and places that they encountered along the way. While the Pacific circuit generated a range of responses and served a variety of ends, within its capacious framework I seek to develop three broad and related themes. The first centers on the workings and transnational trajectory of the U.S. culture industry, which ensured that U.S. entertainers assumed a prominent and profitable position on the developing circuit. The second theme looks at how the performances of U.S. entertainers in transnational contexts were dynamic interactions imbued with cross-cultural meaning and long-term impacts. Lastly, the dissertation explores the complex relationship between the evolving Pacific circuit and an expanding U.S. empire. The analysis proceeds from the first circuses and minstrel troupes that embarked on transpacific tours in the early 1850s through the emergence of an increasingly integrated and expansive entertainment circuit in the 1870s. Noteworthy figures covered include General Tom Thumb, Harry Kellar, James Bailey, and the Georgia Minstrels, amongst many others. The Pacific circuit linked together an ever-increasing and shifting set of cultural markets and while Australia was the most significant, U.S. entertainers also visited Hawai’i, New Zealand, Japan, and major colonial ports like Singapore, Hong Kong, and Batavia. Ultimately, this study of the making of the Pacific circuit, and the entertainers that enlivened it, argues that the U.S. culture industry fabricated an “Empire of Culture” in the nineteenth-century Pacific world.Ph.D.American CultureUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75991/1/mwittman_1.pd

A local resampling trick for focused molecular dynamics

We describe a method that focuses sampling effort on a user-defined selection of a large system, which can lead to substantial decreases in computational effort by speeding up the calculation of nonbonded interactions. A naive approach can lead to incorrect sampling if the selection depends on the configuration in a way that is not accounted for. We avoid this pitfall by introducing appropriate auxiliary variables. This results in an implementation that is closely related to configurational freezing and elastic barrier dynamical freezing. We implement the method and validate that it can be used to supplement conventional molecular dynamics in free energy calculations (absolute hydration and relative binding)

Neural activity tracking identity and confidence in social information

Humans learn about the environment either directly by interacting with it or indirectly by seeking information about it from social sources such as conspecifics. The degree of confidence in the information obtained through either route should determine the impact that it has on adapting and changing behaviour. We examined whether and how behavioural and neural computations differ during non-social learning as opposed to learning from social sources. Trial-wise confidence judgements about non-social and social information sources offered a window into this learning process. Despite matching exactly the statistical features of social and non-social conditions, confidence judgements were more accurate and less changeable when they were made about social as opposed to non-social information sources. In addition to subjective reports of confidence, differences were also apparent in the Bayesian estimates of participants' subjective beliefs. Univariate activity in dorsomedial prefrontal cortex and posterior temporoparietal junction more closely tracked confidence about social as opposed to non-social information sources. In addition, the multivariate patterns of activity in the same areas encoded identities of social information sources compared to non-social information sources

The simplest demonstrations of quantum nonlocality

We investigate the complexity cost of demonstrating the key types of nonclassical correlations-Bell inequality violation, Einstein, Podolsky, Rosen (EPR)-steering, and entanglement-with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known Clauser-Horne-Shimony-Holt test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require nonprojective measurements. The simplest EPR-steering test requires a choice of projective measurement for one agent and a single nonprojective measurement for the other, while the simplest entanglement test uses just a single nonprojective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular two-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment

Neural mechanisms for learning self and other ownership

The sense of ownership – of which objects belong to us and which to others - is an important part of our lives, but how the brain keeps track of ownership is poorly understood. Here, the authors show that specific brain areas are involved in ownership acquisition for the self, friends, and strangers