Related papers: 500-th solution of 2D Ising model
The paper considers the generalized Ising model in the $2\times2\times\infty$ strip with a Hamiltonian invariant with respect to the central axis of rotation through the angle $\pi/2$, which includes all possible multiplicative interactions…
We introduce an algebraic formula producing infinitely many exact solutions of the constant astigmatism equation $ z_{yy} + ({1}/{z})_{xx} + 2 = 0 $ from a given seed. A construction of corresponding surfaces of constant astigmatism is then…
A linearized version of Heisenberg's fundamental equation is solved, and the solutions satisfy the axioms of a relativistic quantum field theory with a fundamental length.
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
The damage spreading method (DS) provided a useful tool to obtain analytical results of the thermodynamics and stability of the 2D Ising model --amongst many others--, but it suffered both from ambiguities in its results and from large…
In our recent paper, we classified plane symmetric kinematic self-similar perfect fluid and dust solutions of the second, zeroth and infinite kinds. However, we have missed some solutions during the process. In this short communication, we…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
We show that the center of mass of Ising vectors that obey some simple constraints, is again an Ising vector.
In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for a hierarchy of integrable difference equations. We also provide an example of such a solution that is related to sequence generated…
The solvation force for the 2D Ising strip is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical surface fields, and the antisymmetric case to exactly opposite surface…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
In this case study, we illustrate the great potential of experimental mathematics and symbolic computation, by rederiving, ab initio, Onsager's celebrated solution of the twodimensional Ising model in zero magnetic field. Onsager's…
A previously tested differential equation method for generating low temperature series expansion for diagonal spin-spin correlation functions in the d=2 Ising model is extended to generate the non-universal terms for arbitrary separation of…
The solution of one Zamfiresku's problem was obtained. We discuss the unsolved questions related to the Mizel's problem.
We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines.
The use of a transfer matrix method to solve the 3D Ising model is straightforwardly generalized from the 2D case. We follow B.Kaufman's approach. No approximation is made, however the largest eigenvalue cannot be identified. This problem…
The critical 2-dimensional Ising model is studied with four types boundary conditions: free, fixed ferromagnetic, fixed antiferromagnetic, fixed double antiferromagnetic. Using Bond Propagation algorithms with surface fields, we obtained…
In this paper, we will investigate the solvability of the equation $x_1^k + x_2^k + \ldots + x_s^k = n$, $n\in \mathbb{Z}_{p^k}$, $x_1,...,x_s\in \mathcal{A}$, $\mathcal{A}\subseteq \mathbb{Z}_{p^k}$. We will give a upper bound of the…
We study the two-dimensional Ising model with a defect line and evaluate multipoint energy correlation functions using non-perturbative field-theoretical methods. We also discuss the evaluation of the two spin correlator on the defect line.
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.