相关论文: Multi-point local height probabilities of the CSOS…

We compute the spontaneous staggered polarization of the cyclic SOS model at the thermodynamic limit. We use the determinant representation for finite-size form factors obtained from algebraic Bethe Ansatz.

We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe Ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state…

In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.

By using the bosonization technique, we derive an integral representation for multi-point Local Hight Probabilities for the Andrews-Baxter-Forrester model in the regime III. We argue that the dynamical symmetry of the model is provided by…

An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic…

We shall consider sections of an elliptic scheme $\mathcal{E}$ over a(n affine) base curve $B$, and study the points of $B$ where the section takes a torsion value. In particular, we shall relate the distribution in $B$ of these points with…

The height probabilities for the recurrent configurations in the Abelian Sandpile Model on the square lattice have analytic expressions, in terms of multidimensional quadratures. At first, these quantities have been evaluated numerically…

Quadratic Chabauty is a $p$-adic method for determining rational points on curves. Local heights are arithmetic invariants used in the quadratic Chabauty method. We present an algorithm to compute these local heights for hyperelliptic…

We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions…

Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…

We consider the $L$-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer…

The quantum mechanical concept of quasi-exact solvability is based on the idea of partial algebraizability of spectral problem. This concept is not directly extendable to the systems with infinite number of degrees of freedom. For such…

We compute the lattice 1-site probabilities, on the upper half-plane, of the four height variables in the two-dimensional Abelian sandpile model. We find their exact scaling form when the insertion point is far from the boundary, and when…

We study the problem of describing local components of height functions on abelian varieties over characteristic $0$ local fields as functions on spaces of torsors under various realisations of a $2$-step unipotent motivic fundamental group…

We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…

We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical…

We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field…

This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…

For the whole set of dilogarithm identities found recently using the thermodynamic Bethe-Ansatz for the $ADET$ series of purely elastic scattering theories we give partition identities which involve characters of those conformal field…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…