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Journal ArticleDOI

Ordering, metastability and phase transitions in two-dimensional systems

12 Apr 1973-Journal of Physics C: Solid State Physics (IOP Publishing)-Vol. 6, Iss: 7, pp 1181-1203
TL;DR: In this article, 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, and 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.
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.
Citations
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Journal ArticleDOI
TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Abstract: This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

6,601 citations

Journal ArticleDOI
TL;DR: In this article, the authors reviewed the Bose-Einstein condensation of dilute gases in traps from a theoretical perspective and provided a framework to understand the main features of the condensation and role of interactions between particles.
Abstract: The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

4,782 citations

Journal ArticleDOI
TL;DR: In this article, the most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned, and a review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data.
Abstract: This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

3,926 citations

Journal ArticleDOI
TL;DR: In this article, a wide list of topics ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading are reviewed and connections between these problems and other, more traditional, topics of statistical physics are highlighted.
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.

3,840 citations

Journal ArticleDOI
TL;DR: In this article, the authors examined the methods used to synthesize transition metal dichalcogenides (TMDCs) and their properties with particular attention to their charge density wave, superconductive and topological phases, along with their applications in devices with enhanced mobility and with the use of strain engineering to improve their properties.
Abstract: Graphene is very popular because of its many fascinating properties, but its lack of an electronic bandgap has stimulated the search for 2D materials with semiconducting character. Transition metal dichalcogenides (TMDCs), which are semiconductors of the type MX2, where M is a transition metal atom (such as Mo or W) and X is a chalcogen atom (such as S, Se or Te), provide a promising alternative. Because of its robustness, MoS2 is the most studied material in this family. TMDCs exhibit a unique combination of atomic-scale thickness, direct bandgap, strong spin–orbit coupling and favourable electronic and mechanical properties, which make them interesting for fundamental studies and for applications in high-end electronics, spintronics, optoelectronics, energy harvesting, flexible electronics, DNA sequencing and personalized medicine. In this Review, the methods used to synthesize TMDCs are examined and their properties are discussed, with particular attention to their charge density wave, superconductive and topological phases. The use of TMCDs in nanoelectronic devices is also explored, along with strategies to improve charge carrier mobility, high frequency operation and the use of strain engineering to tailor their properties. Two-dimensional transition metal dichalcogenides (TMDCs) exhibit attractive electronic and mechanical properties. In this Review, the charge density wave, superconductive and topological phases of TMCDs are discussed, along with their synthesis and applications in devices with enhanced mobility and with the use of strain engineering to improve their properties.

3,436 citations

References
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Journal ArticleDOI
TL;DR: In this paper, 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.
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.

6,236 citations

Journal ArticleDOI
P. C. Hohenberg1
TL;DR: In this paper, it was shown that a rigorous inequality first proved by Bogoliubov may be used to rule out the existence of quasi-averages (or long-range order) in Bose and Fermi systems for one and two dimensions.
Abstract: It is pointed out that a rigorous inequality first proved by Bogoliubov may be used to rule out the existence of quasi-averages (or long-range order) in Bose and Fermi systems for one and two dimensions and $T\ensuremath{ e}0$.

1,730 citations

Book
01 Jan 1964
TL;DR: In this article, a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space, is studied, and the author considered this high degree of specialization worth while because of the theory of such random walks is far more complete than that of any larger class of Markov chains.
Abstract: This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worth while, because of the theory of such random walks is far more complete than that of any larger class of Markov chains. The book will present no technical difficulties to the readers with some solid experience in analysis in two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential and integral operators. There are almost 100 pages of examples and problems.

1,605 citations

Journal ArticleDOI
TL;DR: In this paper, the authors generalized Bose-Einstein condensation to a system of interacting particles and showed that B.E. condensation is present whenever the largest eigenvalue of the one-particle reduced density matrix is an extensive rather than an intensive quantity.
Abstract: The mathematical description of B.E. (Bose-Einstein) condensation is generalized so as to be applicable to a system of interacting particles. B.E. condensation is said to be present whenever the largest eigenvalue of the one-particle reduced density matrix is an extensive rather than an intensive quantity. Some transformations facilitating the practical use of this definition are given.An argument based on first principles is given, indicating that liquid belium II in equilibrium shows B.E. condensation. For absolute zero, the argument is based on properties of the ground-state wave function derived from the assumption that there is no "long-range configurational order." A crude estimate indicates that roughly 8% of the atoms are "condensed" (note that the fraction of condensed particles need not be identified with $\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}$). Conversely, it is shown why one would not expect B.E. condensation in a solid. For finite temperatures Feynman's theory of the lambda-transition is applied: Feynman's approximations are shown to imply that our criterion of B.E. condensation is satisfied below the lambda-transition but not above it.

1,224 citations

Journal ArticleDOI
N. D. Mermin1
TL;DR: In this article, it was shown that the Fourier component of the density must vanish in the thermodynamic limit, provided that the pair potential is in equilibrium in a parallelogram box.
Abstract: If $N$ classical particles in two dimensions interacting through a pair potential $\ensuremath{\Phi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ are in equilibrium in a parallelogram box, it is proved that every $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{ e}0$ Fourier component of the density must vanish in the thermodynamic limit, provided that $\ensuremath{\Phi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})\ensuremath{-}\ensuremath{\lambda}{r}^{2}|{\ensuremath{ abla}}^{2}\ensuremath{\Phi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})|$ is integrable at $r=\ensuremath{\infty}$ and positive and nonintegrable at $r=0$, both for $\ensuremath{\lambda}=0$ and for some positive $\ensuremath{\lambda}$. This result excludes conventional crystalline long-range order in two dimensions for power-law potentials of the Lennard-Jones type, but is inconclusive for hard-core potentials. The corresponding analysis for the quantum case is outlined. Similar results hold in one dimension.

1,113 citations