The Odd Eight-Vertex Model
نویسندگان
چکیده
منابع مشابه
3 The odd eight - vertex model
We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered 8-vertex model. Using this equivalence we deduce the solution of the odd 8-vertex ...
متن کاملNew Developments in the Eight Vertex Model II. Chains of odd length
We study the transfer matrix of the 8 vertex model with an odd number of lattice sites N. For systems at the root of unity points η = mK/L with m odd the transfer matrix is known to satisfy the famous “TQ” equation where Q(v) is a specifically known matrix. We demonstrate that the location of the zeroes of this Q(v) matrix is qualitatively different from the case of even N and in particular the...
متن کاملAnalytic theory of the eight-vertex model
We observe that the exactly solved eight-vertex solid-on-solid model contains an hitherto unnoticed arbitrary field parameter, similar to the horizontal field in the six-vertex model. The parameter is required to describe a continuous spectrum of the unrestricted solid-onsolid model, which has an infinite-dimensional space of states even for a finite lattice. The introduction of the continuous ...
متن کاملThe Eight Vertex Model. New results
Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T . We describe the construction of eigenvectors of T corresponding to degenerate eigenvalues and discuss the related hidden elliptic symmetry.
متن کاملComplexity Classification of the Eight-Vertex Model
We prove a complexity dichotomy theorem for the eight-vertex model. For every setting of the parameters of the model, we prove that computing the partition function is either solvable in polynomial time or #P-hard. The dichotomy criterion is explicit. For tractability, we find some new classes of problems computable in polynomial time. For #P-hardness, we employ Möbius transformations to prove ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2004
ISSN: 0022-4715
DOI: 10.1023/b:joss.0000037206.47155.58