Polynomial Growth for Birational Mappings from Four-State Spin Edge Models
نویسندگان
چکیده
منابع مشابه
Polynomial Growth for Birational Mappings from Four-State Spin Edge Models
We classify all four-state spin edge models according to their behavior under a specific group of birational symmetry transformations generated from the so-called inversion relations. This analysis uses the measure of complexity of the action of birational symmetries of these lattice models, and aims at uncovering (star-triangle) solvable ones. One finds that these spin edge models have biratio...
متن کاملIntegrable Mappings and Polynomial Growth
We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These invo-lutions correspond respectively to two kinds of transformations on q × q matrices: the inversion of the q × q matrix and an (involutive) permutation of the entries of the matrix. We concentrate on the...
متن کاملFour-state ferroelectric spin-valve
Spin-valves had empowered the giant magnetoresistance (GMR) devices to have memory. The insertion of thin antiferromagnetic (AFM) films allowed two stable magnetic field-induced switchable resistance states persisting in remanence. In this letter, we show that, without the deliberate introduction of such an AFM layer, this functionality is transferred to multiferroic tunnel junctions (MFTJ) all...
متن کاملUnsigned State Models for the Jones Polynomial
It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we sh...
متن کاملSimple Birational Extensions of the Polynomial Algebra
The Abhyankar-Sathaye Problem asks whether any biregular embedding φ : C →֒ C can be rectified, that is, whether there exists an automorphism α ∈ AutC such that α ◦ φ is a linear embedding. Here we study this problem for the embeddings φ : C3 →֒ C4 whose image X = φ(C3) is given in C4 by an equation p = f(x, y)u + g(x, y, z) = 0, where f ∈ C[x, y]\{0} and g ∈ C[x, y, z]. Under certain additional ...
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 Nonlinear Mathematical Physics
سال: 2003
ISSN: 1776-0852
DOI: 10.2991/jnmp.2003.10.s2.11