N. D. Mermin

Bio: N. D. Mermin is an academic researcher from Cornell University. The author has contributed to research in topics: Bell's theorem & Quantum nonlocality. The author has an hindex of 16, co-authored 22 publications receiving 7850 citations.

Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models

Abstract: It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.

Extreme quantum entanglement in a superposition of macroscopically distinct states

Abstract: A Bell inequality is derived for a state of n spin-1/2 particles which superposes two macroscopically distinct states. Quantum mechanics violates this inequality by an amount that grows exponentially with n.

Circulation and Angular Momentum in the A Phase of Superfluid Helium-3

Abstract: It is shown that the curl of the velocity field generally identified with v/sub s/ in the A phase of superfluid $sup 3$He is entirely determined in the absence of singularities by the spatial gradients of the order-parameter symmetry axis 1. As a simple application of this relation it is argued that, in a texture of cylindrical symmetry in a volume V, the liquid should have a nonvanishing thermal-equilibrium orbital angular momentum of order rho/sub s/Vh/M. (AIP)

Detector inefficiencies in the Einstein-Podolsky-Rosen experiment

Abstract: The question of how to deal with inefficient detectors in actual experiments of the Einstein-Podolsky-Rosen type is studied. We derive the necessary and sufficient condition for compatibility with local realism of data collected in experiments with two settings of each detector, without making auxiliary assumptions about undetected events. For the conventional experiment with particles in the singlet state (or its photon analogue), the data predicted by the quantum theory do not violate this condition unless the quantum efficiency of the detectors exceeds 83%.

Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s

Abstract: The quantitative quantum-mechanical analysis of the Einstein-Podolsky-Rosen experiment for correlated particles of arbitrary spin $s$ is shown to contradict a generalized form of Bell's inequality, for suitable orientations of the detectors. As the classical ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) limit is approached, the range of angles for which the contradiction arises vanishes as $\frac{1}{s}$.

Phase Transitions and Critical Phenomena

Abstract: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies. Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

Quantum entanglement

Abstract: All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory} But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding However, it appeared that this new resource is very complex and difficult to detect Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon A basic role of entanglement witnesses in detection of entanglement is emphasized

Ordering, metastability and phase transitions in two-dimensional systems

Abstract: A new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists. The possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation. The critical behaviour found in this model displays very weak singularities. The application of these ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid are discussed. This type of phase transition cannot occur in a superconductor nor in a Heisenberg ferromagnet.

The structure of suspended graphene sheets

Abstract: Graphene — a recently isolated one-atom-thick layered form of graphite — is a hot topic in the materials science and condensed matter physics communities, where it is proving to be a popular model system for investigation. An experiment involving individual graphene sheets suspended over a microscale scaffold has allowed structure determination using transmission electron microscopy and diffraction, perhaps paving the way towards an answer to the question of why graphene can exist at all. The 'two-dimensional' sheets, it seems, are not flat, but wavy. The undulations are less pronounced in a two-layer system, and disappear in multilayer samples. Learning more about this 'waviness' may reveal what makes these extremely thin carbon membranes so stable. Investigations of individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or in air reveal that the membranes are not perfectly flat, but exhibit an intrinsic waviness, such that the surface normal varies by several degrees, and out-of-plane deformations reach 1 nm. The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles1,2,3. However, the physical structure of graphene—a single layer of carbon atoms densely packed in a honeycomb crystal lattice—is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment4,5,6,7,8,9. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix1,2,3,9,10,11,12. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals13,14,15.

Statistical physics of social dynamics

Abstract: Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.