Lax Pairs for Integrable Six-Vertex Model with Color Parameters

Using the colored Yang-Baxter equation, the Lax pairs for the system with color parameters and periodic boundary conditions are derived. The explicit expressions of the Lax pairs for the six-vertex standard R matrices of both the Baxter and free-Fermion types are given.     

The sl2 Loop Algebra Symmetry of the Six-Vertex Model at Roots of Unity

We demonstrate that the six vertex model (XXZ spin chain) with =(q+q^-1)/2 and q^2N=1 has an invariance under the loop algebra of sl₂ which produces a special set of degenerate eigenvalues. For =0 we compute the multiplicity of the degeneracies using Jordan–Wigner techniques.     

Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model with a non-diagonal reflecting end under domain wall boundary condition.     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.     

The Arctic Curve of the Domain-Wall Six-Vertex Model

The problem of the form of the ‘arctic’ curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of q-enumerated (with 0<q ≤4) large alternating sign matrices. In particular, as q→0 the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.     

Convergence of the Stochastic Six-Vertex Model to the ASEP

In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for arbitrary initial data.     

A stochastic model of three-dimensional crystal growth

This paper describes a stochastic model of crystallization from a gas or dilute solution. The model is limited to a crystal of rectangular symmetry whose surface has nonzero Miller indices. By a mapping into the modified KDP model, the kinetic growth coefficient can be given approximately as an analytic function of the Miller indices of the surface. Numerical simulations indicate that the aproximation is accurate within a few percent at all surface orientations.     

Completeness of the Bethe Ansatz for the Six and Eight-Vertex Models

We discuss some of the difficulties that have been mentioned in the literature in connection with the Bethe ansatz for the six-vertex model and XXZ chain, and for the eight-vertex model. In particular we discuss the beyond the equator, infinite momenta and exact complete string problems. We show how they can be overcome and conclude that the coordinate Bethe ansatz does indeed give a complete set of states, as expected.     

开边界六顶角模型的边界关联函数

讨论了具有开边界六顶角模型的关联函数，计算了涉及边界自发极化的边界关联函数，得到了它们的行列式表示. 关键词： 六顶角模型 关联函数 开边界     

Symmetry ensemble theory of spin wave emitting effectdriven by current in nanoscale magnetic multilayer

<正>This paper proposes a symmetry ensemble model for the magnetic dynamics caused by spin transfer torque in nanoscale pseudo-spin-valves,in which individual spin moments in the free layer are considered as subsystems to form a spinor ensemble.The magnetization dynamics equation of the ensemble was developed.By analytically investigating the equation,many magnetization dynamics properties excited by polarized current reported in experiments,such as double spin wave modes and the abrupt frequency jump,can be successfully explained.It is pointed out that an external field is not necessary for spin wave emitting(SWE) and a novel perpendicular configuration structure can provide much higher SWE efficiency in zero magnetic field.     

Rigorous derivation of domain growth kinetics without conservation laws

The time evolution of the Ising model that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops atT=0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we show that the average lifetime of such a domain is proportional to its area. We also consider theT=0 dynamics of a single infinite quadrant. The area of the quadrant decreases during the time evolution, and we show that the area lost grows linearly with time. We solve a first passage time problem as well. That is, we calculate the average time it takes for the area lost to reach a given value for the first time. Lastly, we map the infinite quadrant model onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical six-vertex model.     

The asymmetric six-vertex model

The exact solution of the asymmetric six-vertex model, published nearly without derivation by Sutherlandet al. in 1967, is rederived in detail. The transfer matrix method and the Bethe Ansatz solution for the free energy (which can be calculated from an integral equation) are discussed. For some special cases (zero or maximal polarization) the integral equation can be solved exactly. In addition, an asymptotic analysis, valid for small but nonzero polarization, is carried out. The analytical properties of the results and their relevance for the BCSOS model are discussed.     

The Bethe ansatz for the six-vertex model with rotated boundary conditions

A method is suggested for derivation of the Bethe ansatz equations for the six-vertex model on a square lattice rotated at an arbitrary angle with respect to the coordinate axes. The method is based on the random walk representation for configurations of the model. The equations for the ice model on the rotated lattice are derived and some numerical results are obtained.     

从Sn质子滴线核到Sn中子滴线核的自旋对称性和赝自旋对称性

在球形相对论平均场模型下, 采用NLSH相互作用全面研究了从Sn质子滴线核到Sn中子滴线核的自旋对称性和赝自旋对称性. 发现: 1) 随着核子数的增大, 中子和质子的赝自旋波函数劈裂基本上都是减小的, 并且质子的变化趋势更加明显. 中子高能级的自旋波函数劈裂随着核子数的增大也是减小的. 2) 对于特定的同位素, 当n=1时, 赝自旋波函数劈裂随着l的增大而增大. 当n=2时, 中子的自旋波函数劈裂随着l的增大而增大. 当l=2或l=3时, 中子的自旋波函数劈裂随着n的增大而增大. 3) 中子和质子的赝自旋劈裂之间的差别总是比自旋劈裂的差别更大一些.     

Discrete Symmetry Breaking for Certain Short-Range Interactions

Georgii's theorem ensures that, restricted to two-dimensional planes, a single ocean (i.e., infinite connected component) of a ground state and islands (i.e., finite connected components) are observed in lattice spin systems at sufficiently low temperature. This paper extends his results for higher dimensional hyperplanes. Our proof is mainly based on a kind of Peierls argument and is different from Georgii's, which relies on the percolation method.     

New Correlation Duality Relations for the Planar Potts Model

We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.     

Variational Bounds for the Generalized Random Energy Model

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds,” and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature regime using Talagrand’s concentration of measure inequality, and in the low temperature regime using convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction. While the argument for the lower bound is fairly standard, our proof of the upper bound is new.