Ising model

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

Time ordering and the thermodynamics of strange sets: Theory and experimental tests.

Abstract: From the spectrum of dimensions of a fractal invariant measure of a dynamical system one can extract information about the dynamical process that gave rise to the measure This is equivalent to finding the class of Hamiltonians of an Ising model with a given thermodynamics

Mixed spin-12 and spin-32 Blume–Capel Ising ferrimagnetic system on the Bethe lattice

Abstract: We present the exact formulation for the mixed spin - 1 2 and spin - 3 2 Blume–Capel Ising ferrimagnetic system on the Bethe lattice by the use of exact recursion relations. The exact expressions for the magnetization, quadrupole moment, Curie temperature and free energy are found and the phase diagrams are illustrated on the Bethe lattice with the coordination numbers q = 3 , 4, 5 and 6. It is found that the phase diagram of this mixed spin system only presents second-order phase transitions. The thermal variation of the magnetization belonging to each sublattice and the net magnetization are also presented.

Long-range Ising and Kitaev models: phases, correlations and edge modes

Abstract: We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the one-dimensional Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance r as , as well as a related class of fermionic Hamiltonians that generalize the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents α, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for , while connected correlation functions can decay with a hybrid exponential and power-law behavior, with a power that is α-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every α. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough α. For the fermionic models we show that the edge modes, massless for , can acquire a mass for . The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.

Two-dimensional periodic frustrated ising models in a transverse field

Abstract: We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase transitions or to a quantum spin liquid (cooperative paramagnetic) phase as in the triangular and kagome lattice antiferromagnets, respectively. For the latter, we further predict passage to a bond-ordered phase followed by a critical phase as the field is tilted. These systems also provide exact realizations of quantum dimer models introduced in studies of high temperature superconductivity.

Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

Abstract: We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one dimension. At the critical point the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single continuously varying exponent, ${z}^{\ensuremath{'}}$, which diverges at the critical point, as in one dimension. Consequently, the zero temperature susceptibility diverges for a range of parameters about the transition.