Antiferromagnetic Heisenberg chain

Fig. 17. Free energy (F), entropy (S) and specific heat (C) of an A = 10 site antiferromagnetic Heisenberg chain. Solid line correspond to the MC results, indistinguishable from the dotted lines for the exact results. Also shown is the relative error s F) of F compared to the exact result...

Excitations of the antiferromagnetic Heisenberg chain of U atoms with spin 1/2 are examined. It is found that the energy of the lowest lying excitations for a total spin 3 and wave number q converges to 1f/2 sinq as N- oo,if s[Pg.67]

Fig. 19. Susceptibility versus temperature for the antiferromagnetic Heisenberg chain. N is the number of sites in the chain (58).

By means of the known numerical results for antiferromagnetic Heisenberg chains with S=i [110] and S=1 [109] as well as the exact result for S-+oo [107], the unknown quantities a, b and d may be determined, each one as a function of temperature. In this way, the magnetic susceptibility curves for any particular spin value are obtained. 

Figure 5 Diamagnetic rings currents, Nx z), of half-filled Pariser-Parr-Pople models for regular polygons with D h symmetry. The dashed line at 2 = U/4 t0 = 1.17 corresponds to standard parameters z = 0 is the Hiickel limit of free electrons, while z 1 is the strong-correlation limit of antiferromagnetic Heisenberg spin chain with vanishing ring currents [50].

Hydrates. A2MnmF5 H20 compounds (A = K, Rb, Cs) are suitable examples of Heisenberg chain antiferromagnets. The 1-D behavior is enhanced by the ferrodistortive ordering of dj2 orbitals, antiparallel along the c direction. In the ab plane weak d°2 y2 interactions occur between the chains. 

The chain of 1/2 spins coupled by nearest neighbour antiferromagnetic Heisenberg interaction is one of the most widely investigated quantum-mechanical model systems. 

The temperature dependence of the susceptibility is well-described by the alternating chain antiferromagnetic Heisenberg model. 

Cu(py)2Cl2 p 80-2 Farad Heisenberg antiferromagnetic linear chains TIP estimated as 74D21,... 

Farad antiferromagnetic linear chain magnetism fitted according to the Heisenberg model for T>10 K and according to Bonner and Fisher for T<10 K using J/k=( —3.2 0.2) K... 

Fig.103. Mn(py)2Br2. Temperature dependence of x m-Curves fitted according to antiferromagnetic Heisenberg linear-chain model full curve best fit according to Weng s interpolation scheme (J/k= —0.85 0.02 JSC) dashed curve best fit according to the scaling method...

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