Is there a way to write the entropy of a Heisenberg model Hamiltonian?
See the book "Statistical Mechanics of Magnetically Ordered Systems" by Yu. A. Izyumov and Yu. N. Skryabin, Consultants Bureau, New York (1988), p. 30.
To understand the book you must know about diagram and Green function technique. The book is theoretically oriented.
A slightly more understandable book is "Spin Waves", by A.I. Akhiezer, V.G. Bar'yakhtar, and S.V. Peletminskii, North Holland (1968), p. 201.
What do you mean by writing the entropy...?
In principle you could compute, for instance using computer simulation, the
internal (potential) energy, U, and the Helmholtz "free" energy, A, using the so-called thermodynamic integration, both as functions of temperature T,
Then using the thermodynamic relation: A = U - TS, you get the entropy, S.
Anyway, I guess you are asking something else.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
Some ferromagnetic and anti-ferromagnetic spin systems are studied in the literature where interaction Hamiltonian is H= -JA Σi∈A j∈A Si.Sj -JB Σi∈B j∈B Si.Sj -J0 Σi∈A j∈B Si.Sj Such systems are divided into two blocks as A and B. Block entanglement entropy can be calculated in such cases, when there is long range magnetic order in the ground state. Entropy grows logarithmically with block size.
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