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WarnK
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Homework Statement
1D polymer, fixed segment length a
If the angle between segment j and j+1 is 0, the energy is 0
If the angle is pi the energy is +2J.
Compute the correlation function [tex]<s_i s_{i+n}>[/tex], where [tex]s_j = \pm 1[/tex] denotes the direction of segment j
Find the persistence length Lp, defined through
[tex]<s_i s_{i+n}> = e^{-|n|a/Lp} [/tex]
Find an expression for the end-to-end distance [tex]S(N) = <(x_N - x_0)^2>^{1/2}[/tex] as a function of temperature and the number of links N
Homework Equations
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The Attempt at a Solution
[tex]<s_i s_{i+n}> = \frac{ Tr s_i s_{i+n} e^{-\beta H} }{ Tr e^{-\beta H} }[/tex]
But I don't know any hamiltonian? Or even what sort of trace to do.
The problem sort of reminds me of the 'XY'-modell for spins on a 1d lattice, but I don't really understand how to make any use of that.
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