Partition functions of classical Heisenberg spin chains with arbitrary and different exchange

Abstract

The classical Heisenberg model has been effective in modelling exchange interactions in molecular magnets. In this model, the partition function is important as it allows the calculation of the magnetization and susceptibility. For an ensemble of N-spin sites, this typically involves integrals in 2N dimensions. Here, for two-, three-and four-spin nearest neighbour open linear Heisenberg chains these integrals are reduced to sums of known functions, using a result due to Gegenbauer. For the case of the three-and four-spin chains, the sums are equivalent in form to the results of Joyce. The general result for an N-spin chain is also obtained.

Two dimensional magnetic correlation in the unconventional corrugated layered oxides (Ba,Sr)4Mn3O10

“…Considering trimerized Mn 3 O 12 building blocks of the compounds, we have analyzed the data with the isolated linear spin-trimer model. From the theoretical point of view this model is applicable for isolated 3-spin system where the spin quantum number is large (S 3/2) [13][14][15][16]. The Hamiltonian for a isolated 3-spin blocks in presence of an external magnetic field H can be written as:…”

Two dimensional magnetic correlation in the unconventional corrugated layered oxides (Ba,Sr)$_4$Mn$_3$O$_{10}$

“…From the theoretical point of view this model is applicable for isolated 3-spin system where spin quantum number is large (S ≥ 3/2). [13][14][15][16] The Hamiltonian for a isolated 3-spin blocks in presence of an external magnetic field H can be written as:…”