Ising model

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

Monte Carlo studies of the dipolar spin ice model

Abstract: We present a detailed overview of numerical Monte Carlo studies of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy2Ti2O7 and Ho2Ti2O7. We show that the dipolar spin ice model can reproduce an effective quasi-macroscopically degenerate ground state and spin ice behaviour of these materials when the long range nature of dipole–dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long range ordered state is identified via Monte Carlo simulation techniques. Finally, we investigate the behaviour of the dipolar spin ice model in an applied magnetic field and compare our predictions to experimental results. We find that a number of different long range ordered ground states are favoured by the model, depending on field direction.

Conformal Field Theories in Fractional Dimensions

Abstract: We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of ϕ^4 theory in the ϵ expansion.

Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite

Abstract: Krypton atoms adsorbed in submonolayer quantities onto the basal graphite surface may be represented by a triangular lattice gas with nearest-neighbor exclusion and further-neighbor attraction decreasing with separation. We view this as a three-state Potts model with thermodynamic vacancies which are controlled by a chemical potential. A position-space renormalization-group treatment is performed by adapting Migdal's approximate recursion to the triangular lattice, and results are compared with experimental data. Our temperature versus density phase diagram for krypton submonolayers has an in-registry solid phase separated from a liquid phase by a line of continuous (Potts tricritical) transitions at higher temperatures. At lower temperatures, the solid phase is separated from a gas phase by first-order transitions. The Potts tricritical line meets the coexistence region of the first-order transitions at an isolated fourth-order transition point. This point may be related to the transition of the triplet Ising model, solved exactly by Baxter and Wu. Our "Potts lattice gas" global phase diagram is in a three-parameter space of pair-interaction constants and chemical potential. It contains solid, liquid, and gas phases, variously separated by first-order, Ising critical, three- and four-state Potts, and fourth-order transitions. The Lennard-Jones potential between krypton adatoms determines the planar subspace applicable to krypton submonolayers. Other planes, similarly determined, are applicable to adsorbed nitrogen, methane, and ethane, for which we estimate the temperatures of the fourth-order points. Our treatment also predicts a tricritical end-point topology, instead of the fourth-order point topology, when second-neighbor adatom pair attraction is not much stronger than third- and fourth-neighbor attractions.

In-plane electronic anisotropy of underdoped '122' Fe-arsenide superconductors revealed by measurements of detwinned single crystals

Abstract: The parent phases of the Fe-arsenide superconductors harbor an antiferromagnetic ground state. Significantly, the Neel transition is either preceded or accompanied by a structural transition that breaks the four-fold symmetry of the high-temperature lattice. Borrowing language from the field of soft condensed matter physics, this broken discrete rotational symmetry is widely referred to as an Ising nematic phase transition. Understanding the origin of this effect is a key component of a complete theoretical description of the occurrence of superconductivity in this family of compounds, motivating both theoretical and experimental investigation of the nematic transition and the associated in-plane anisotropy. Here we review recent experimental progress in determining the intrinsic in-plane electronic anisotropy as revealed by resistivity, reflectivity and angle-resolved photoemission spectroscopy measurements of detwinned single crystals of underdoped Fe-arsenide superconductors in the '122' family of compounds.

Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory

Abstract: The transfer matrix of the XXZ open spin-½ chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q| = 1) is diagonalized using the representation theory of the q-Onsager algebra. Similarly to the Ising and superintegrable chiral Potts models, the complete spectrum is expressed in terms of the roots of a characteristic polynomial of degree d = 2N. The complete family of eigenstates are derived in terms of rational functions defined on a discrete support which satisfy a system of coupled recurrence relations. In the special case of linear relations between left and right boundary parameters for which Bethe-type solutions are known to exist, our analysis provides an alternative derivation of the results of Nepomechie et al and Cao et al. In the latter case the complete family of eigenvalues and eigenstates splits into two sets, each associated with a characteristic polynomial of degree d < 2N. Numerical checks performed for small values of N support the analysis.