New Developments in the Eight Vertex Model II. Chains of Odd Length
New Developments in the Eight Vertex Model II. Chains of Odd Length
复制标题
八顶点模型 II 的新进展。
DOI：
10.1007/s10955-005-4410-5
复制
发表时间：
2004
影响因子：
1.6
通讯作者：
B. McCoy
中科院分区：
文献类型：
--
作者：
K. Fabricius;B. McCoy
摘要：研究奇数8顶点模型的传递矩阵
晶格点数N.
对于统一点根处的系统 η=mK/L 且 m
奇数传输矩阵已知满足
著名的“TQ”方程，其中 Q(υ) 是一个特别已知的矩阵。我们证明了零点的位置
这个 Q(υ) 矩阵与
EvenN 的情况，特别是它们满足一个先前未知的方程，该方程更
比通常所说的“贝特方程”更一般。对于偶数的情况
m，其中 Q(υ) 矩阵未知
我们证明，有许多状态不是从形式主义中获得的
SOS 模型但满足 TQ 方程。的基态为
详细研究了 η=2K/3 和 N odd 的特殊情况。
AbstractWe study the transfer matrix of the 8 vertex model with an odd
number of lattice sites N.
For systems at the root of unity pointsη=mK/L with m
odd the transfer matrix is known to satisfy the
famous ‘‘TQ’’ equation where Q(υ) is a specifically known matrix. We demonstrate that the location of the zeroes of
this Q(υ) matrix is qualitatively different from the
case of evenN and in particular they satisfy a previously unknown equation which is more
general than what is often called ‘‘Bethe’s equation.’’ For the case of even
m where no Q(υ) matrix is known
we demonstrate that there are many states which are not obtained from the formalism of the
SOS model but which do satisfy the TQ equation. The ground state for the
particular case of η=2K/3 and N odd is investigated in detail.