Magnetization of a Gapped Spin 1/2 Antiferromagnetic Ising Chain near the Critical External Field

We study the magnetization of gapped spin 1/2 XXZ Heisenberg Ising chains and calculate the scattering length among massive spinons. We obtain the magnetization close to the critical external magnetic field. The leading correction term determined by the scattering length among massive spinons is given. Our results are in agreement with exact results and with experimental results. We show that the deviation from the massive free hard core boson picture can be accounted very well by the leading correction term due to the spinon-spinon interaction. We show that the deviation increases along with the increasing of the Ising term.     

Differential equation for local magnetization in the boundary Ising model

We show that the local magnetization in the massive boundary Ising model on the half-plane with boundary magnetic field satisfies second order linear differential equation whose coefficients are expressed through Painleve function of the III kind.     

Fermion-Spin Approach to Study the Doping Dependence of Antiferromagnetism in the Copper Oxide Material

Within the fermion-spin theory, we study the ground-state properties of the copper oxide materials by considering quantum fluctuations of spinons in the random-phaseapproximation (RPA). The RPA ground-state at half-filling is the magnetized π-flux state with the energy E₀=-0.332J per bond and the staggered magnetization M = 0.327. Away from half-fiing this staggered magnetization vanishes around doping δ= 5% for the reasonable parameter t/J = 5, which is in very good agreement with the experiments on copper oxide materials. Our results indicate that both hole dopings and quantum fluctuations of spinons lead to a strong suppression of the antiferromagnetic long-range order.     

Finite-size scaling for the ising model on the Möbius strip and the klein bottle

We study the finite-size scaling properties of the Ising model on the M?bius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function p(m) for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at T = T(c) for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.     

Spontaneous magnetizations of the Ising model on the union Jack lattice

We demonstrate that the (Union-Jack lattice) Ising model maps onto an isotropic free-fermion eight vertex model. Using this result we show the claim of Lin and Lee, that the spontaneous magnetization given by Vaks, Larkin and Ovchinnikov is in error, to be incorrect. By the use of correlation identities for the checkerboard Ising model, we derive the mean spontaneous magnetization on the Union-Jack lattice, which agrees with low-temperature series expansion.     

Critical Point of the Honeycomb Antiferromagnetic Ising Model in a Nonzero Magnetic Field: An Analytical Analysis

In this paper we determined the critical point of the antiferromagnetic Ising model in a nonzero magnetic field on the honeycomb lattice by an analytical method-the generalized cumulant expansion with the mean field hypothesis. By calculating the magnetization to the fourth order correction, we get encouraging results when compared with the known numerical results by finite size analysis.     

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.     

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.     

Quantum corrections to the energy density of a homogeneous Bose gas

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of , where is the number density and a is the S-wave scattering length. We calculate the ground state energy density to second order in . The coefficient of the correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on a, but also on an extra parameter that describes the low energy scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is ,and is the length scale set by the van der Waals potential. Received 2 February 1999     

Correlation effects in small-angle multiple neutron scattering

The dependence of the spectra of small-angle multiple neutron scattering on the volume fraction occupied by scattering grains is considered. The concentration expansion is used to develop scattering theory in the eikonal approximation. The leading term of the expansion reproduces the standard low-concentration theory (Mollier). Some properties of the first correction term are analyzed, and it is shown that the angular distribution narrows with an increase in concentration, in qualitative agreement with the experimental data.     

Numerical investigation of logarithmic corrections in two-dimensional spin models

The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional four-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to the algebraic decay exhibited in these models. A conformal mapping is used to relate the finite-geometry information to that of the infinite plane. Extraction of the leading singularity is altered by the expected logarithmic corrections, and we show numerically that both leading and correction terms are mutually consistent.     

Algebraic Reduction of the Ising Model

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.     

Quantum relaxation after a quench in systems with boundaries

We study the time dependence of the magnetization profile, m(l)(t), of a large finite open quantum Ising chain after a quench. We observe a cyclic variation, in which starting with an exponentially decreasing period the local magnetization arrives to a quasistationary regime, which is followed by an exponentially fast reconstruction period. The nonthermal behavior observed at near-surface sites turns over to thermal behavior for bulk sites. In addition to the standard time and length scales a nonstandard time scale is identified in the reconstruction period.     

Ordering in Ising models of parabolic shape

The features of order in narrow systems are studied for isotropic square lattice Ising models with general parabolic boundaries. Using Monte Carlo methods, magnetization profiles are calculated which agree very well with the conformal results and scale properly with the geometrical length parameter. The variation of the tip magnetization with temperature is obtained and the predicted stretched exponential form in the critical region is confirmed.     

Expansion Around the Mean Field in Quantum Magnetic Systems

We introduce a new definition of ordered phase in a magnetic system based on properties of the local spin state probability. A statistical functional associated to this quantity depends both on amplitude and direction of the local magnetization. We show that it is possible to introduce an expansion at fixed magnetization amplitude in the inverse of lattice coordination number if the direction is selected by an extremum condition. In the limit of infinite coordination number we recover the mean field results. First order corrections are derived for the Ising model in the presence of a transverse field and for the XY model. Our results concerning critical temperature and order parameter compare favorably with other approaches.     

Reduction of surface coverage of finite systems due to geometrical steps

The coverage of vicinal, stepped surfaces with molecules is simulated with the help of a two-dimensional Ising model including local distortions and an Ehrlich-Schwoebel barrier term at the steps. An effective two-spin model is capable to describe the main properties of this distorted Ising model. It is employed to analyze the behavior of the system close to the critical points. Within a well-defined regime of bonding strengths and Ehrlich-Schwoebel barriers we find a reduction of coverage (magnetization) at low temperatures due to the presence of the surface step. This results in a second, low-temperature transition besides the standard Ising order-disorder transition. The additional transition is characterized by a divergence of the susceptibility as a finite-size effect. Due to the surface step the mean-field specific heat diverges with a power law.     

A new approach to the study of effective string corrections in LGTs

We propose a new approach to the study of the interquark potential in Lattice Gauge Theories. Instead of looking at the expectation value of Polyakov loop correlators we study the modifications induced in the chromoelectric flux by the presence of the Polyakov loops. In abelian LGTs, thanks to duality, this study can be performed in a very efficient way, allowing to reach high precision at a reasonable CPU cost. The major advantage of this strategy is that it allows us to eliminate the dominant effective string correction to the interquark potential (the Lüscher term) thus giving an unique opportunity to test higher order corrections. Performing a set of simulations in the 3d spin Ising model and then translating the result in the 3d gauge Ising model using duality, we were thus able to precisely identify and measure both the quartic and the sextic effective string corrections to the interquark potential. While the quartic term perfectly agrees with the Nambu–Goto one the sextic term is definitely different. Our result seems to disagree with the recent proof of the universality of the sextic correction. We discuss a few possible explanations of this disagreement.     

Motion of bound domain walls in a spin ladder

The elementary excitation spectrum of the spin- \frac12\frac{1}{2} antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension d > 1, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin- \frac12\frac{1}{2} AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.     

Spectral function of a quarter-filled one-dimensional charge density wave insulator

We consider a one-dimensional charge density wave insulator formed by umklapp processes in a quarter-filled band. The spectrum of the model consists of gapless, uncharged excitations carrying spin +/- 1/2 (spinons) and gapped, spinless excitations carrying charge -/+ signe/2 (solitons and antisolitons). We calculate the low-energy behavior of the single-electron Green's function at zero temperature. The spectral function exhibits a featureless scattering continuum of two solitons and many spinons. The theory predicts that the gap observed by angle resolved photoemission is twice the activation gap in the dc conductivity. We comment on possible applications to PrBa(2)Cu(3)O(7) and to the Bechgaard salts.