Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.

Ising Model on a Triangular Lattice with Three-spin Interactions. I. The Eigenvalue Equation

Abstract: It is shown that the Ising model with three-spin interactions on a triangular lattice is equivalent to a site-colouring problem on a hexagonal lattice. The transfer matrix method is then used to solve the colouring problem. The colouring of two neighbouri

History of the Lenz-Ising Model 1920–1950: From Ferromagnetic to Cooperative Phenomena

Abstract: I chart the considerable changes in the status and conception of the Lenz-Ising model from 1920 to 1950 in terms of three phases: In the early 1920s, Lenz and Ising introduced the model in the field of ferromagnetism. Based on an exact derivation, Ising concluded that it is incapable of displaying ferromagnetic behavior, a result he erroneously extended to three dimensions. In the next phase, Lenz and Ising’s contemporaries rejected the model as a representation of ferromagnetic materials because of its conflict with the new quantum mechanics. In the third phase, from the early 1930s to the early 1940s, the model was revived as a model of cooperative phenomena. I provide more detail on this history than the earlier accounts of Brush (1967) and Hoddeson, Schubert, Heims, and Baym (1992) and question some of their conclusions. Moreover, my account differs from these in its focus on the development of the model in its capacity as a model. It examines three aspects of this development: (1) the attitudes on the degree of physical realism of the Lenz-Ising model in its representation of physical phenomena; (2) the various reasons for studying and using it; and (3) the effect of the change in its theoretical basis during the transition from the old to the new quantum mechanics. A major theme of my study is that even though the Lenz-Ising model is not fully realistic, it is more useful than more realistic models because of its mathematical tractability. I argue that this point of view, important for the modern conception of the model, is novel and that its emergence, while perhaps not a consequence of its study, is coincident with the third phase of its development.

Entanglement entropy of two disjoint blocks in XY chains

Abstract: We study the Renyi entanglement entropies of two disjoint intervals in XY chains. We exploit the exact solution of the model in terms of free Majorana fermions and we show how to construct the reduced density matrix in the spin variables by taking properly into account the Jordan-Wigner string between the two blocks. From this we can evaluate any Renyi entropy of finite integer order. We study in details critical XX and Ising chains and we show that the asymptotic results for large blocks agree with recent conformal field theory predictions if corrections to the scaling are included in the analysis correctly. We also report results in the gapped phase and after a quantum quench.

Absence of an Almeida-Thouless line in three-dimensional spin glasses

Abstract: We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast with the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.

An Introduction to the Theory of Spin Glasses and Neural Networks

Abstract: The Ising magnetic systems physics of the spin glass state replica method replica symmetry breaking physics of the replica symmetry breaking replica symmetry breaking solution near Tc ultrametricity scaling in the space of spin glass states experiments partial annealing statistical models of neural networks the Hopfield model partial annealing in neural networks other kinds of neural networks. Appendix: stability of the replica-symmetric solutions.