Character decomposition of Potts model partition functions. II. Toroidal geometry

临界三态Ising链的Bethe方程与环形边界条件

Bethe equations for the critical three-state Potts spin chain with toroidal boundary conditions

本文通过Bethe方程参数化临界三态Potts链的谱，揭示低能激发态自旋的分数特性，并提出构建混合环形边界条件的可积哈密顿量方法。

Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice

We present exact calculations of the partition function of the q-state Potts model for general q and temperature on strips of the square lattice of width L_y=3 vertices and arbitrary length L_x with periodic longitudinal boundary conditions, of the following types: (i) (FBC_y,PBC_x)= cyclic, (ii) (FBC_y,TPBC_x)= Möbius, (iii) (PBC_y,PBC_x)= toroidal, and (iv) (PBC_y,TPBC_x)= Klein bottle, where FBC and (T)PBC refer to free and (twisted) periodic boundary conditions. Results for the L_y=2 torus and Klein bottle strips are also included. In the infinite-length limit the thermodynamic properties …

Eigenvalue amplitudes of the Potts model on a torus

We consider the Q-state Potts model in the random-cluster formulation, defined on finite two-dimensional lattices of size L x N with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N) cannot be written simply as a trace of the transfer matrix T\_L. Using a combinatorial method, we establish the decomposition Z(L,N) = \sum\_{l,D\_k} b^{l,D\_k} K\_{l,D\_k}, where the characters K\_{l,D\_k} = \sum\_i (λ\_i)^N are simple traces. In this decomposition, the amplitudes b^{l,D\_k} of the eigenvalues λ\_i of T\_L are labelled by the number l=0,1,...,L o…

Character decomposition of Potts model partition functions. I. Cyclic geometry

We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L x N, with boundary conditions that are free in the L-direction and periodic in the N-direction. The decomposition of the partition function in terms of the characters K\_{1+2l} (with l=0,1,...,L) has previously been studied using various approaches (quantum groups, combinatorics, transfer matrices). We first show that the K\_{1+2l} thus defined actually coincide, and can be written as traces of suitable transfer matrices in the cluster picture. We then proceed to similarly decom…

一维$q$态修正Potts模型及其热力学函数

One-dimensional $q$-state modified Potts model and its thermodynamic functions

本文研究一维$q$态修正Potts模型，利用转移矩阵方法推导出自由能、熵、磁化强度等热力学量的精确表达式，并分析其参数依赖及极限行为，揭示模型的热力学特性与应用潜力。

On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models

We consider general cyclic representations of the 6-vertex Yang-Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov-Stroganov model and the corresponding chiral Potts model on finite size lattices. We first determine the propagator operator in terms of the chiral Potts transfer matrices and we compute the scalar product of separate states (including the transfer matrix eigenstates) as a single determinant formulae in the framework of Sklyanin's quantum separation of variables. Then, we solve the quantum inverse problem and reconstruct the local operators in terms…