Abstract
An even-site spins- linear chain of cyclic in the nearest-neighbour and next-nearest-neighbour interactions has necessarily a three-ring structure. In this study, the interactions are considered to be short-range through the coupling constants J and K, respectively. For an arbitrary even number of spins-, the exact classical solution of the partition function and the pair correlations between the nearest- and next-nearest-neighbours are calculated in terms of the constants J and K, without using the energy levels and their degeneracy factors. Then, this partition function is used to verify the validity of an ansatz on the allowed energies of the chain and their corresponding degeneracy factors. The influence of next-nearest-neighbour interactions K on the specific heat capacity per spin at the low-temperatures is analysed for the ferromagnetic and antiferromagnetic chains. We especially show that specific heat capacity exhibits the spin frustration when the ferromagnetic and antiferromagnetic orders are demanded via the coupling constants J and K, respectively. Also, the maximal frustration is obtained analytically by two distinct ground levels for even number of spins-.
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