Related papers: A method of calculation for the determinant of the…
By using a decomposition of the transfer matrix of the $q$-state Potts Model on a three dimensional $ m \times n \times n $ simple cubic lattice its determinant is calculated exactly. By using the calculated determinants a formula is…
A finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature and critical exponent of the symmetric and the asymmetric two-layer three-state Potts Models. For similar intralayer…
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…
Since its introduction, the Potts model has gained widespread popularity across various fields due to its diverse applications. Even minor advancements in this model continue to captivate scientists worldwide, and small modifications often…
We establish the Bethe equation of the $\tau^{(2)}$-model in the $N$-state chiral Potts model (including the degenerate selfdual cases) with alternating vertical rapidities. The eigenvalues of a finite-size transfer matrix of the chiral…
A formula is presented for the determinant of the second additive compound of a square matrix in terms of coefficients of its characteristic polynomial. This formula can be used to make claims about the eigenvalues of polynomial matrices,…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
We have calculated the large-$q$ series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the $q$-state Potts model in two…
We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on cyclic and M\"obius strip graphs $G$ of the square (sq), triangular…
This article evaluates the determinants of two classes of special matrices, which are both from a number theory problem. Applications of the evaluated determinants can be found in [arXiv:math.NT/0509523]. Note that the two determinants are…
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…
In our previous work we have shown that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial P_B(q,v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic…
The large-q expansions of the exponential correlation length and the second moment correlation length for the q-state Potts model in two dimensions are calculated at the first order phase transition point both in the ordered and disordered…
In this paper, in continuation of our work, on the determinants of cubic -matrix of order 2 and order 3, we have analyzed the possibilities of developing the concept of determinant of cubic-matrix with three indexes, studying the…
The critical exponents of the four-state Potts model are directly derived from the exact expressions for the latent heat, the spontaneous magnetization, and the correlation length at the transition temperature of the model.
We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.
We consider the two-dimensional dilute q-state Potts model on its first order phase transition surface for 0<q\leq 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of…
The superintegrable chiral Potts model has many resemblances to the Ising model, so it is natural to look for algebraic properties similar to those found for the Ising model by Onsager, Kaufman and Yang. The spontaneous magnetization M_r…
Three-dimensional (3D) $q$-state Potts models ($q$=3, 4, and 5) are studied by the tensor product variational approach (TPVA), which is a recently developed variational method for 3D classical lattice models. The variational state is given…
Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of matrices which are obtained by amalgamating the entries of two smaller matrices. In particular, this gives formulae for…