Continuum Conversion of Lattice Points via Taylor Series Expansion

[saravanan13]

I consider an array of lattice points and construct a vector at each lattice points.
How to convert this discrete system into a continuum one by using the Taylor series expansion by considering the lattice distance say \lambda?

thanks in well advance?

 

[micromass]

I'm afraid you're making no sense to me...

Care to give some more information?

 

[saravanan13]

I meant to say mostly Taylor series is regarded as transformation from discrete system to continuous one. In that sense how can I convert the discrete lattice to continuum one under certain approximation?
This type of problem one can observe spin excitation in the form of magnons and soliton under low temperature and long wavelength limit.
So all the spins in the lattice I consider as a spin vector with lattice distance lambda.
This spin can excite in the low temperature and long wavelength limit and excitation in the form of magnons or solitons.