Topic
Exponential decay
About: Exponential decay is a research topic. Over the lifetime, 6493 publications have been published within this topic receiving 140153 citations.
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Papers
TL;DR: In this paper, a theory of dislocation-mediated melting in two dimensions is described in detail, with an emphasis on results for triangular lattices on both smooth and periodic substrates, and the behavior of the specific heat, structure factor, and various elastic constants near these transitions is worked out.
Abstract: A theory of dislocation-mediated melting in two dimensions is described in detail, with an emphasis on results for triangular lattices on both smooth and periodic substrates. The transition from solid to liquid on a smooth substrate takes place in two steps with increasing temperatures. Dissociation of dislocation pairs first drives a transition out of a low-temperature solid phase, with algebraic decay of translational order and long-range orientational order. This transition is into a "liquid-crystal" phase characterized by exponential decay of translational order, but power-law decay of sixfold orientational order. Dissociation of disclination pairs at a higher temperature then produces an isotropic fluid. The behavior of the specific heat, structure factor, and various elastic constants near these transitions is worked out. We also discuss the applicability of our results to melting on a periodic substrate. Dislocation unbinding should describe melting of a "floating" (and, in general, incommensurate) adsorbate solid into a high-temperature fluid phase. The orientation bias imposed by the substrate can alter or eliminate the disclination-unbinding transition, however. Transitions from a floating solid into a low-temperature registered or partially registered phase can also be mapped onto the dislocation-unbinding transition, but only at certain special values of the coverage. Substrate reciprocallattice vectors play the role of Burger's vectors in this case.
2,382 citations
TL;DR: In this article, an efficient Monte Carlo algorithm for simulating a "hardly relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced.
Abstract: We propose an efficient Monte Carlo algorithm for simulating a “hardly-relaxing” system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.
2,313 citations
TL;DR: In this article, the consequences of dislocation-mediated two-dimensional melting are worked out for triangular lattices, and the critical behavior, as well as the effect of a periodic substrate, is discussed.
Abstract: The consequences of a theory of dislocation-mediated two-dimensional melting are worked out for triangular lattices. Dissociation of dislocation pairs first drives a transition into a "liquid crystal" phase with exponential decay of translational order, but power-law decay of sixfold orientational order. A subsequent dissociation of disclination pairs at a higher temperature then produces an isotropic fluid. The critical behavior, as well as the effect of a periodic substrate, is discussed.
1,930 citations
TL;DR: In this paper, an efficient Monte Carlo algorithm for simulating a ''hardly-relaxing'' system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced.
Abstract: We propose an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional $\pm J$ Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.
1,861 citations
TL;DR: The first rigorous example of an isotropic model in such a phase is presented in this paper, where the Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but the model has a unique ground state and exponential decay of the correlation functions in the ground state.
Abstract: Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.
1,697 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 41 |
| 2024 | 70 |
| 2023 | 137 |
| 2022 | 470 |
| 2021 | 246 |
| 2020 | 266 |