三维精确可解统计模型──Baxter–Bazhanov模型的可积性条件

从手征Potts模型推导出三维精确可解Baxter-Bazhanov模型的“可逆性”及“星一方”关系,从而说明其可积性条件──四面体方程是手征Potts模型星──三角关系的一个结论.若把玻尔兹曼权参变数表示为Zamolodchikov角变量形式,其附加条件自然成立.值得指出的是,由本文处理方法可以得出三维可解统计模型的星-三角关系,它包含了Bazhanov和Baxter的结论.     

三维精确可解格点模型

对Baxter-Bazhanov三维精确可解格点模型玻尔兹曼权Sk间的变换关系作了仔细讨论,并给出了局域可积性条件──三维星-星关系的一个完整证明.     

描述大形变核中对力的硬核Bose-Hubbard模型

讨论了一种描述大形变偶偶核邻近轨道对力相互作用近似的硬核Ｂｏｓｅ－Ｈｕｂｂａｒｄ模型．利用代数方法得到了该模型对激发谱和相应波函数的严格解．该结果可推广到具有任意自旋和有限格点的硬核Ｂｏｓｅ－Ｈｕｂｂａｒｄ和Ｆｅｒｍｉ－Ｈｕｂ－ｂａｒｄ模型中去．     

活动标架系下O（n）非线性σ模型Laxpair矩阵的Poisson—Lie结构

在活动标架系下给出了Ｏ（ｎ）／Ｏ（ｎ－１）对称空间上非线性σ模型的Ｐｏｉｓｓｏｎ－Ｌｉｅ括号，并用协变分解的方法讨论了活动标架与固定标架系的协交关系，得到的ｒ、ｓ矩阵可以明显地看出其依赖于场量的部分是由于Ｓｎ－１流形上的联络引起的．     

三维十五点格子Boltzmann模型仿真

格子气和格子Ｂｏｌｔｚｍａｎｎ方法的迅速发展提供了一类求解流体力学问题的新方法。格子Ｂｏｌｔｚｍａｎｎ方法在保留了格子气模型优点的同时,克服了它的不足之处。本文讨论了一种三维十五点格子Ｂｏｌｔｚｍａｎｎ模型,通过选择适当的平衡分布及参数,并用Ｃｈａｐｍａｎ－Ｅｎｓｋｏｇ展开和多尺度技术导出了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程．在微机上模拟了工程中比较常见的管排绕流问题,并与实验观察到的结果进行了比较,结果表明该模型能较好的模拟复杂流动现象,并具有较好的工程应用背景。     

双光子Jaynes—Cummings模型中的Schrodinger cat态

计算了双光子Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ模型场熵的演化，结合光子数统计分布和位相分布论证了双光子Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ模型在强场情况和某些特定时刻存在“Ｓｃｈｒｏｄｉｎｇｅｒ ｃａｔ”态的迭加态。     

一个经典完全可积的非共形约束的SL(2,R)Wess-Zumino-Novikov-Witten模型(Ⅰ)

通过在ＳＬ（２，Ｒ）Ｗｅｓｓ－Ｚｕｍｉｎｏ－Ｎｏｖｉｋｏｖ－Ｗｉｔｔｅｎ（缩写为ＷＺＮＷ）模型中加入破坏共形对称性的约束，获得了一个新的经典完全可积的二维场论体系，它把著名的ｓｉｎｈ－Ｇｏｒｄｏｎ方程作为其特例。这个广义ｓｉｎｈ－Ｇｏｒｄｏｎ体系的特点是完全可积性和可超定域化，并且描写这些特点的ｒ矩阵是杨－Ｂａｘｔｅｒ方程（经典的）的一个解，它反对称，依赖于两个谱参数，但通过Ｌｏｏｐ代数的自同构变换和谱参数的重新定义后，此ｒ矩阵仍是依赖于一个谱参数的三角型ｒ矩阵。 关键词：     

在Jaynes—Cummings模型中压缩真空初态场位相演化特性

应用Ｐｅｇｇ－Ｂａｒｎｅｔｔ位相理论，研究了Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ模型（Ｊ－Ｃ模型）中压缩真空初态场位相演化特性，具体计算了弱压缩条件下，场的位相几率分布函数及位相涨落，给出了在极坐标中位相几率分布演化曲线，讨论了原子与场相互作用对场的位相性质的影响。     

与压缩真空相互作用的具有强度耦合的广义Kaynes—Cummings模型 …

考虑具有强度耦合的广义Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ模型与压缩真空相互作用。根据Ｐｅｇｇ和Ｂａｍｅｔｔ新的相位理论,不仅得到了压缩真空场的相位分布,相位期待值和相位涨落的普遍表示式,及其演化图示,而且还导出了弱压缩真空和强压缩真空情形的近似角极表示式。对于压缩真空的压缩量与相位特性之间的关系进行了简要讨论。     

在Jaynes－Cummings模型中压缩真空初态场位相演化特性

应用Ｐｅｇｇ－Ｂａｒｎｅｔｔ位相理论，研究了Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ模型（Ｊ－Ｃ模型）中压缩真空初态场位相演化特性，具体计算了弱压缩条件下，场的位相几率分布函数及位相涨落，给出了在极坐标中位相几率分布演化曲线，讨论了原子与场相互作用对场的位相性质的影响。     

Remarks on the star-triangle relation in the Baxter-Bazhanov model

We show that the restricted star-triangle relation introduced by Bazhanov and Baxter can be obtained either from the star-triangle relation of the chiral Potts model or from the star-square relation proposed by Kashaev, Mangazeev, and Stroganov, and give a response to a guess of Bazhanov and Baxter.     

Star-triangle relation for a three-dimensional model

The solvablesl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. We show that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly.On leave of absence from the Institute for High Energy Physics, Protvino, Moscow Region, 142284, Russia.     

Integrable boundary Boltzmann weights and surface free energy inversion relations of the chiral Potts model

The integrability of the chiral Potts model with boundaries is considered in this paper. The boundary star-triangle relation determining the boundary Boltzmann weights for the chiral Potts model is presented. By solving the boundary star-triangle relation the boundary Boltzmann weights are obtained. The fusion procedure is then applied to derive the functional relations of the transfer matrices of the model with boundaries. From these functional relations the inversion relations of the surface free energies are extracted when the system size is big enough. Surprisingly, the inversion relation of the local surface free energy is as simple as those of other non-chiral models, but it has still to be solved.     

Equivalence of the Two Results for the Free Energy of the Chiral Potts Model

The free energy of the chiral Potts model has been obtained in two ways. The first used only the star-triangle relation, symmetries, and invariances, and led to a system of equations that implicitly define the free energy, and from which the critical behavior can be obtained The second used the functional relations derived by Bazhanov and Stroganov, solving them to obtain the free energy explicitly as a double integral. Here we obtain, for the first time, a direct verification that the two results are identical at all temperatures.     

Critical line of the triangular potts model with two- and three-site interactions: An alternate derivation

A double star-triangle relation which is a generalization of the usual single star-triangle relation is introduced. Together with a duality transformation it is possible to rederive the critical line of the Potts model with two- and three-site interactions on alternate triangles.     

Corner transfer matrices of the chiral Potts model. II. The triangular lattice

We consider a two-dimensional edge-interaction model satisfying the star-triangle relations. For the triangular lattice, the corner transfer matrices are functions of three rapidities: we show that they possess various factorization properties and satisfy certain equations. We indicate how these equations can be solved for the Ising model. We then consider the three-state chiral Potts model and obtain low-temperature solutions to the equations. The conjectured formula for the order parameter (the spontaneous magnetization) is verified to one more order in a series expansion.     

On discrete three-dimensional equations associated with the local Yang-Baxter relation

The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a proper generalization to three dimensions of the zero curvature relation. Recently, Korepanov has constructed an infinite set of integrable three-dimensional lattice models, and has related them to solutions to the local YBE. The simplest Korepanov model is related to the star-triangle relation in the Ising model. In this Letter the corresponding discrete equation is derived. In the continuous limit it leads to a differential three-dimensional equation, which is symmetric with respect to all permutations of the three coordinates. A similar analysis of the star-triangle transformation in electric networks leads to the discrete bilinear equation of Miwa, associated with the BKP hierarchy.Some related operator solutions to the tetrahedron equation are also constructed.St. Petersburg Branch of the Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191011, RussiaURA 14-36 du CNRS, associée à l'ENS de Lyon, au LAPP d'Annecy et à l Universitè de Savoie, France     

Free energy of the solvable chiral Potts model

Very recently, it has been shown that there are chiralN-state Potts models in statistical mechanics that satisfy the star-triangle relation. Here it is shown that the relation implies that the free energy (and its derivatives) satisfies certain functional relations. These can be used to obtain the free energy: in particular, we expand about the critical case and find that the exponent is 1–2/N.     

Chiral Potts model as a descendant of the six-vertex model

We observe that theN-state integrable chiral Potts model can be considered as a part of some new algebraic structure related to the six-vertex model. As a result, we obtain a functional equation which is supposed to determine all the eigenvalues of the chiral Potts model transfer matrix.     

Commuting transfer matrices in the chiral Potts models: Solutions of star-triangle equations with genus>1

We present solutions of the star-triangle equations which are uniformized by curves of genus greater than one. One particular solution which is relevant to the commensurate-incommensurate transition in the chiral three-state Potts model has genus 10 if T≠T_c and genus 1 if T=T_c. Solutions for N>3 are also presented.