Related papers: Derivation of the order parameter of the chiral Po…
An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but as far as the author is…
By using a decomposition of the transfer matrix of the two dimensional $q$-state Potts Model to $V^{\prime}_1$ and $V_2$ its determinant is calculated. Our result is a proof for a conjectured formula by Chang and Shrock in [14].
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
It has been known for some time that the Boltzmann weights of the chiral Potts model can be parametrized in terms of hyperelliptic functions, but as yet no such parametrization has been applied to the partition and correlation functions.…
A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the…
In this paper, we present a systematical account of the descending procedure from six-vertex model to the $N$-state chiral Potts model through fusion relations of $\tau^{(j)}$-operators, following the works of Bazhanov-Stroganov and…
We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the…
In the first part of this paper I shall discuss the round-about way of how the integrable chiral Potts model was discovered about 30 years ago. As there should be more higher-genus models to be discovered, this might be of interest. In the…
In this paper, we prove the conjecture for the coefficients of the two variable generating function used in our previous paper. The conjecture was tested numerically before, but its proof was lacking up to now.
An elementary derivation of the chiral gauge anomaly in all even dimensions is given in terms of noncommutative traces of pseudo-differential operators.
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
We show how $Z$-invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrable eigenvectors. When the distance between the two spins in…
We propose an order parameter for the one dimensional Mott-Hubbard transition and provide numerical evidence and general theoretical arguments for the correctness of our proposal. In addition, we discuss some of the implications of this…
The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the…
In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal…
Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate $\langle…
A one parameter generalization of Ward's chiral model in 2+1 dimensions is given. Like the original model the present one is integrable and possesses a positive-definite and conserved energy and $y$-momentum. The details of the scattering…
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
In this note we are concerned about the generalization of the GHS inequality for the Potts model. We also obtain by a different method the proof of the GHS inequality for the Ising model. We take advantage of a polynomial expansion and we…
We study the derivational complexity induced by the dependency pair method, enhanced with standard refinements. We obtain upper bounds on the derivational complexity induced by the dependency pair method in terms of the derivational…