By Barus C.
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Extra resources for The Elongation Due to Magnetization
14, where J1 , J2 and J3 refer to the three exchange. Since all these couplings are AF, this compound offers a nice example of spin-frustration in one dimension. The magnetic properties show a continuous decrease of χ T upon cooling (Fig. 15). However, the plot of χ vs. T does not show the characteristic maximum down to 2 K, in agreement with the fact that frustration tends to reduce short-range order. 5, tends to disappear when spin-frustration is introduced (antiferromagnetic J1 ) (Fig. 15). 23 K.
23 K. Fig. 14. Theoretical magnetic behavior of the triangular Heisenberg chain for J2 = J3 and different ratios between J1 and J2 . Fig. 15. Magnetic behavior of MnMn(CDTA) · 7H2 O. The solid line represents the best fit to the triangular chain model [57,58]. 1 23 Quantum-classical Heisenberg Ferrimagnetic Chains Alternation of Quantum and Classical Spins: Uniform and Alternating Quantum-classical Chains The first study of a quantum-classical Heisenberg chain was reported by Dembinski & Wydro  for the analysis of the correlation functions and specific heat properties.
Adding an (N + 1)th spin to the N -spin chain, we can similarly define Z N +1 , and Z N +1 . Clearly, Z N +1 is directly related to Z N through a (2s + 1) × (2s + 1) matrix, namely the transfer matrix T: Z N +1 = (T)Z N (43) The current term of (T) is: (T)m N ,m N +1 = exp(β(J m N + gµB B)m N +1 ) (44) which takes into account the exchange coupling between s N and s N +1 , and the Zeeman effect on s N +1 . Clearly, (T) does not depend on N . This recurrence property permits the calculation of the partition vector Z N for arbitrary N , starting from Z0 which is easily determined.
The Elongation Due to Magnetization by Barus C.