Analyticity of correlation functions for the two-dimensional Ising model

Analyticity of correlation functions for the two-dimensional Ising model as a function of the inverse temperature except for the singularity at the critical temperature is proved. A crucial step is the establishment of the correspondence between extremal equilibrium states of the model and pure ground states of a one-dimensional spin system below the critical temperatureT _c . An exact decay rate of the clustering property along axes is also determined for allTT _c .     

Partition function zeros for the two-dimensional Ising model

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated. For anisotropic square and triangular lattices the distribution function is two-dimensional and satisfies a partial differential equation derived from a generalized scaling theory. Corresponding results for the isotropic square, triangular and honeycomb lattices are also presented.     

Many-point correlation functions of the two-dimensional Ising model

We report the results of an exact computation of the arbitrary many-point correlation function formed by p-energy density and q-spin operators for the two-dimensional Ising model.     

On the rotational symmetry of the spin-spin correlation function of the two-dimensional Ising model

The spin-spin correlation function 〈s_oos_mn〉 of the two-dimensional Ising model is derived in the absence of a magnetic field. It is proved rigorously that this correlation function becomes rotationally symmetric near the critical point.     

Monte Carlo study of the Yukawa coupled two-spin Ising model

We consider a particular four state spin system composed of two Ising spins (s_x, σ_x) with independent hopping parameters κ₁ κ₂, coupled by a bilinear Yukawa term, ys_xσ_x. The Yukawa term is solely responsible for breaking the global Z₂ × Z₂ symmetry down to Z2. This model is intended as an illustration of general coupled Higgs system where scalars can arise both as composite and elementary excitations. For the Ising example in 2d, we give convincing numerical evidence of the universality of the two-spin system with the one-spin Ising model, by Monte Carlo simulations and finite size scaling analysis. We also show that as we approach the phase transition, universality arises by having a single correlation length that diverges.     

Remarks on the rotational invariance of two-dimensional Ising model correlation functions

We refute a contention of Bariev concerning the proof of the rotational invariance of Ising model correlation functions.     

Approximate calculations for the two-dimensional Ising model

A self-consistent molecular field approximation for the two-dimensional, square-lattice Ising model is used to calculate the energy and magnetization. Agreement with the exact calculations is good except near the critical temperature, which differs from the exact critical temperature by 4%. The specific heat has no anomalous behavior asT approachesT _c from above, and the magnetization follows the incorrect Weiss (T _c-T)^1/2 law asT approachesT _c from below.     

The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc

The form-factor bootstrap approach is used to compute the exact contributions in the large-distance expansion of the correlation function 〈σ(x)σ(0)〉 of the two-dimensional Ising modeliin a magnetic field at T = T_c The matrix elements of the magnetization operator σ,(x) present a rich analytic structure induced by the (multi-)) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.     

The direct correlation function of a one-dimensional Ising model

The strictly finite range of the direct correlation function for a homogeneous nearest neughbor Ising chain is shown to persist in the presence of arbitrary site-dependent coupling constants and an arbitrary external field. A method is developed to examine the range of the direct correlation function for many-neighbor interactions. It is found from numerical examples that, in general, third-neighbor and higher interactions induce long-range direct correlations, as does the presence of a field in the second-neighbor case.     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. II.T>T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects aboveT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

Manifestly finite perturbation theory for the short-distance expansion of correlation functions in the two-dimensional Ising model

We review and apply the recently proposed formalism for the study of the theory space of euclidean quantum field theories based on the variational formula to the analysis of the scaling limit of the two-dimensional massive Ising model. An extension of the first-order variational formula to higher orders provides a manifestly finite scheme for the perturbative calculation of the operator product coefficients to any order in parameters. A perturbative expansion of the correlation functions follows. We implement this scheme for a systematic study of correlation functions involving two spin operators. We show how the necessary non-trivial integrals can be calculated. As two concrete examples we explicitly calculate the short-distance expansion of the spin-spin correlation function to third order and the spin-spin-energy-density correlation function to first order in the mass. We also comment on how our results may be applied to perturbations of non-trivial fixed points corresponding to other unitary minimal models.     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. I.T<T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects belowT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

Two site spin correlation function in Bethe-Peierls approximation for Ising model

Two site spin correlation function for an Ising model above Curie temperature has been calculated by generalising Bethe-Peierls approximation. The results derived by a graphical method due to Englert are essentially the same as those obtained earlier by Elliott and Marshall, and Oguchi and Ono. The earlier results were obtained by a direct generalisation of the cluster method of Bethe, while our results are derived by retaining that class of diagrams, which is exact on Bethe lattice.     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点.本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究.系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长.通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界...     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点。本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究。系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长。通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界指数在数值上却存在很大差异,相差一个 =1,这是由初始条件导致的。     

Upper bounds for Ising model correlation functions

A Griffiths correlation inequality for Ising ferromagnets is refined and is used to obtain improved upper bounds for critical temperatures. It is shown that, for non-negative external fields, the mean field magnetization is an upper bound for the magnetization of Ising ferromagnets.On leave (1970–71) from Northwestern University, Evanston, Illinois 60201. Supported at IAS by a grant from the Alfred P. Sloan Foundation.     

Exact solution of a general two-dimensional Ising model: The partition function

The exact partition function per spin is obtained for a two-dimensional generalization of the Ising model. This general model consists of a unitary cell that is repeated throughout the system. The unitary cell is made up of spins in t columns and q rows with arbitrary energies between them. The exact result is given in terms of certain Ψ quantities (see section 2), which can be determined for particular cases.

It is always possible to transform the unit cell in order to obtain a desired given model. Thus, the results for several known models are recovered, e.g., the Utiyama and the hexagonal (with three different interaction parameters) models. Furthermore, explicit results are presented for other models hitherto not reported in the literature, as are the general hexagonal (with six different interaction parameters), the general triangular model (with six different interaction parameters) and the tetragonal-triangular (with seven different interaction parameters) models.     

On the correlation functions of fully frustrated two-dimensional Ising systems

By mapping the triangular antiferromagnet, the Villain model and the Union-Jack model on the quantumXY-chain we show a simple way to obtain the exponent =1/2 for the decay of the spin-correlation function at the frustration points of these models. A similar procedure for the Baxter model leads to non-universal values of .