Ising Version Research Articles

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.

Contribution of vibronic interactions to the thermodynamics of the phase transition in H-bonded ferroelectrics: Proton-lattice coupling effects in crystals of the KDP family

A model Hamiltonian for microscopic description of structural phase transitions in KDP type ferroelectrics was considered in terms of the vibronic theory of heteroligand systems (VTHS). The Hamiltonian contains three terms that describe the proton interactions, the potential energy of lattice oscillators, and the relationship between these subsystems. In the second order perturbation theory, the configuration energies of the Bethe cluster method retained the Ising form, with the pseudospin Hamiltonian parameters explicitly depending on the electronic structure characteristics and the vibronic constants of the AO4-containing structural units. The Ising version of the theory was used for obtaining the numerical estimations of the thermodynamic properties, in particular, the critical temperature Tc as a function of all the parameters of the pseudospin Hamiltonian.

Proton-lattice coupling and vibronic effects in KDP-family thermodynamics

Based on the vibronic theory of heteroligand complexes a new model Hamiltonian is proposed for the ferroelectrics of KDP (KH2PO4) family. In local representation three items of this Hamiltonian describe the H-bond protons, the potential energy of lattice's oscillators and the coupling of these two subsystems respectively. In Ising form, convenient for numerical calculations, the Hamiltonian offered includes explicitly the characteristics of the electronic structure as well as the orbital vibronic constants of the AO4 tetrahedra. The Ising version of theory is then applied to numerical studying of some questions for KDP thermodynamics.

High Speed Signed multiplier for Digital Signal Processing Applications

The speed of a multiplier is of utmost importance to any Digital Signal Processor (DSPs). Along with the speed its precision also plays a major role. Although Floating point multipliers provide required precision they tend to consume more silicon area and are relatively slower compared to fixed point (Q-format) multipliers. In this paper we propose a method for fast fixed point signed multiplication based on Urdhava Tiryakbhyam method of Vedic mathematics. The coding is done for 16 bit (Q15) and 32 bit (Q31) fractional fixed point multiplications using Verilog and synthesized using Xilinx ISE version 12.2. Further the speed comparison of this multiplier with normal booth multiplier and Xilinx LogiCore parallel multiplier Intellectual Property (IP) is presented. The results clearly indicate that Urdhava Tiryakbhyam can have a great impact on improving the speed of Digital Signal Processors.

Effective approach to the Nagaoka regime of the two-dimensionalt-Jmodel

We argue that the t-J model and the recently proposed Ising version of this model give the same physical picture of the Nagaoka regime for J/t << 1. In particular, both models are shown to give compatible results for a single Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the standard t-J or t-Jz models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking the advantage of this fact, we study the low doping regime of t-J model for J/t << 1 and show that the ground state exhibits phase separation into hole-rich ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds true up to a threshold concentration of holes, \delta < \delta_t ~ 0.44 \sqrt{J/t}. Analytical calculations show that \delta_t=\sqrt{J/2\pi t}.

Ising t–J model close to half filling: a Monte Carlo study

Within the recently proposed doped-carrier representation of theprojected lattice electron operators we derive a full Ising version of thet–J model. This model possesses the global discreteZ2 symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants,t and J. In contrast, in the spin anisotropic limit of thet–J model, usuallyreferred to as the t–Jz model, the globalSU(2) invariance isfully restored at Jz = 0, so that only the spin–spin interaction has in this model the true Ising form.We discuss a relationship between these two models and the standard isotropict–J model. We show that the low-energy quasiparticles in all three modelsshare qualitatively similar properties at low doping and small values ofJ/t. The main advantageof the proposed Ising t–J modelover the t–Jz one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to103 sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF)order by doping as well as the interplay between the AF order and hole mobility. We alsodiscuss the effect of the exchange interaction and that of the next-nearest-neighbourhoppings on the destruction of the AF order at finite doping. We show that theshort-range AF order is observed in a wide range of temperatures and dopings,much beyond the boundaries of the AF phase. We explicitly demonstrate that thelocal no-double-occupancy constraint plays the dominant role in destroying themagnetic order at finite doping. Finally, a role of inhomogeneities is discussed.

Temperature cycles in the Heisenberg spin glass

We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the timescale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found numerically in the Ising version of the model, and to experimental results in different samples. We discuss the theoretical interpretations of our findings, arguing, in particular, that `full' rejuvenation can be observed in experiments even if temperature chaos is absent.

Aging dynamics of the Heisenberg spin glass

We numerically study the non-equilibrium dynamics of the three dimensional Heisenberg Edwards-Anderson spin glass following a sudden quench to its low temperature phase. The subsequent aging behavior of the system is analyzed in detail, and the scaling behavior of various space-time correlation functions is investigated for both spin and chiral degrees of freedom. We carefully compare our results with those obtained from simulations of the more studied Ising version of the model, and with experiments on real spin glasses in which the spins have vectorial character. Finally, the present dynamical study offers new perspectives into the possibility of spin-chirality decoupling at low temperature in vectorial spin glasses.

Polymerization in a ferromagnetic spin model with threshold.

We propose a spin model with a new kind of ferromagnetic interaction, which may be called {\it ferromagnetic coupling with threshold}. In this model the contribute of a given spin to the total energy has only two possible values and depends on the number of parallel spins among its nearest and next to the nearest neighbors. By mapping the model onto the Ising version of the isotropic eight vertex model, we obtain some evidence of a low temperature phase made of alternate parallel pluses and minuses polymers.

Polarizations andp-T-phase diagram of bccd: Interpretation in terms of frustrated Ising models

Abstract The observed (pressure, temperature)-phase diagram of betaine-calciumchloride-dihydrate—which exhibits a multitude of phases—and the polarizations of these phases are discussed in terms of the ANNNI model with an improved matching to the crystal structure and of the Ising version of Chen & Walker's model. The experimentally observed shifts of the main phase boundaries under uniaxial pressure and upon substituting part of the Cl ions by Br are explained.

Exact results for randomly decorated magnetic frustrated models of planar CuO2 systems.

We present {ital exact} results for a random {ital annealed} decorated square lattice in which the nodal spin interacts antiferromagnetically ({ital J}{sub {ital A}}{lt}0) with its nearest neighbors and ferromagnetically ({ital J}{gt}0) with a decorated spin on the bond between them. For the {ital n}-vector version of the model, we present an exact calculation of the effective coupling of a decorated bond. Moreover, for the Ising version we obtain exactly the magnetic phase diagram. In particular, we find that this model exhibits a critical decorated bond concentration {ital p}{sub {ital c}}=({minus}{radical}2 /2)/2{congruent}0.1464... above which, for small values of the ratio {vert bar}{ital J}{sub {ital A}}/J{vert bar}, the antiferromagnetic phase ceases to exist, i.e., the paramagnetic phase extends to {ital T}=0. This intriguing exact result for the magnetic phase diagrams may possibly have relevance for the planar copper oxide superconducting materials; although the CuO{sub 2} planes in these materials are believed to be described by quantum Heisenberg spins, our results for the Ising model may capture some of the relevant qualitative physics.

Canonical-ensemble results for the Ising model with random bonds in two dimensions

The purpose of this paper is to show how some interesting numerically exact thermal averages can be computed for finite two-dimensional Ising models by a transfer-matrix method, and to apply these methods to the Ising version of the Edwards-Anderson (EA) model of a spin-glass to ascertain whether there is a phase transition. We do not study the spatial dependence of $〈{\ensuremath{\sigma}}_{0}{\ensuremath{\sigma}}_{l}〉$ for, as we show with an example, its behavior for finite systems can be misleading. It is first shown how to obtain ${\ensuremath{\chi}}_{\mathrm{EA}}^{\ensuremath{'}}$, defined by ${\ensuremath{\chi}}_{\mathrm{EA}}^{\ensuremath{'}}={N}^{\ensuremath{-}1}\ensuremath{\Sigma}{〈{〈{\ensuremath{\sigma}}_{i}{\ensuremath{\sigma}}_{j}〉}_{T}^{2}〉}_{J}$. We compute ${\ensuremath{\chi}}_{\mathrm{EA}}^{\ensuremath{'}}$ and study the quantity $\ensuremath{\Lambda}=\frac{\ensuremath{-}\ensuremath{\partial}\mathrm{ln}({\ensuremath{\chi}}_{\mathrm{EA}}^{\ensuremath{'}})}{\ensuremath{\partial}T}$, both as a function of temperature ($T$) and of the number of spins ($N$) in the system. The results obtained for square systems of up to 100 spins in the case where $J=\ifmmode\pm\else\textpm\fi{}1$ with equal probability and for square systems of up to 121 spins in the case where each $J$ is normally distributed about $J=0$ are in accord with the existence of a critical point at ${T}_{0}\ensuremath{\simeq}1.0$ and at ${T}_{0}\ensuremath{\simeq}0.6$, respectively. In addition the value $\ensuremath{\nu}\ensuremath{\approx}1$ is obtained. The value $q=0$ for $Tg0$ is consistent with the results obtained. The low-temperature entropy per spin ($S$) is computed for long strips of different widths. Extrapolation to an infinite width yields $\frac{S}{k}\ensuremath{\simeq}0.07$. It is also shown how to calculate the probability, $P(\ensuremath{\eta})$, that the quantity, $\ensuremath{\eta}={N}^{\ensuremath{-}1}\ensuremath{\Sigma}{\ensuremath{\tau}}_{i}{\ensuremath{\sigma}}_{i}$, where each ${\ensuremath{\tau}}_{i}=0,\ifmmode\pm\else\textpm\fi{}1$ take any value in the range $1l~\ensuremath{\eta}l~1$. The probability, $P(\ensuremath{\eta})$, obtained for the EA model at low temperatures often has several maxima separated by regions of improbable values of $\ensuremath{\eta}$, as is to be expected of a system with metastable states.