# set5 - Department of Physics The Ohio State University...

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Department of Physics Prof. R. Bundschuh The Ohio State University Fifth Problem Set for Physics 847 (Statistical Physics II) Winter quarter 2004 Important dates: Feb 10 10:30am-12:18pm midterm exam, Mar 16 9:30am-11:18am ±nal exam Due date: Thursday, Feb 12 13. Spin correlations 8 points Consider a one-dimensional lattice with N lattice sites and assume that the i th lattice site has spin s i = ± 1. The Hamiltonian describing this lattice is H = - ε N i =1 s i s i +1 . Assume periodic boundary conditions, so s N +1 s 1 . Compute the correlation function h s 1 s 2 i . How does it behave at very high temperature and at very low temperature? 14. Spin 1 magnet 12 points Consider a lattice of N spins s i which can take values s i ∈ {- 1 , 0 , 1 } . In the absence of an external magnetic ±eld the energy of this system is given by H = - ε X { i,j } s i s j . Apply the mean ±eld approximation to this system. Denote the number of nearest neighbors of a spin by ν . a) At which temperature

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## This note was uploaded on 07/17/2008 for the course PHYS 847 taught by Professor Bundschuh during the Winter '04 term at Ohio State.

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set5 - Department of Physics The Ohio State University...

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