The ̄rst part of this paper discusses the introduction of Jordan-Wigner transformations and the spectrum of the XY model. The second part of the paper is devoted to more advanced aspects of the XY …

Show that if random variables X and Y are uncorrelated, then Var (X + Y) = Var (X) + Var (Y). Note that this is a more general statement than Proposition 12.3 since independent variables are uncorrelated.

xy an angle , where 0 < < =2, to form a new set of x^ ^ y-axes, as shown in Figure 1(a). We would like to determine the coordinates for a point in the plane relative to the two P coordinate systems.

A point on the line is labeled by a single coordinate x, a point in the plane is fixed by 2 coordinates (x,y) and a point in space is determined by three coordinates (x,y,z).

hapter 6 The XY Model Abstract The XY Model is another linear chain of spin-1/2 atoms but with a differ-ent type of exchange interaction in which only the x-components and y-components of the spins are …

Covariance and correlation h means X; Y respectively. The covariance, denoted with cov(X; Y ), is a measure of the as De nition: cov(X; Y ) = E(X X)(Y Y )

Fact: Straight lines in (X, Y, Z) space project to straight lines in (x, y) chromaticity space. Proof: Let C1 = (X1, Y1, Z1) and C2 = (X2, Y2, Z2) be two different colors, and let C3 = (X3, Y3, Z3) fall on a line …