Statistical Mechanics of Lattice Systems pp 93-118 | Cite as

# Antiferromagnets and Other Magnetic Systems

Chapter

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## Abstract

The Ising model ferromagnet can be transformed to an antiferromagnet by changing
which is the same as in the ferromagnet for even

*J*to −*J*(*J*> 0) in the configurational energy expression (2.63). The analysis of the one-dimensional case in Chap. 2 remains valid, and replacing*J*by −*J*the zero-field correlation relation (2.88) becomes$$\left\langle {{\sigma _i}{\sigma _{i + k}}} \right\rangle = {( - 1)^k}{[\tanh (J/T)]^k},$$

(4.1)

*k*, but is reversed in sign for odd*k*. At low temperatures the regions of local order are blocks of alternate spins, and nearest-neighbour pairs of parallel spins are the local fluctuations which form the boundaries between these regions. As will be shown in Sect. 4.2, the equilibrium state at*H*= 0 for the antiferromagnet can be obtained from that of the ferromagnet by reversing every other spin, (see Fig. 4.1). The values of*U, F*, and hence*S*, at*H*= 0 are unaltered by the change*J*→ −*J*, as can be seen from (2.81) and (2.82). The zero-field heat capacity given by (2.83) is also unaffected.## Keywords

Ising Model Compensation Point Paramagnetic State Spontaneous Magnetization Critical Curve
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1999