Can someone name a paper or book which calculates the critical temperature of the Ising model from scratch? It might be a book and should contain the necessary prerequisites. I have had a basic course in stat physics and thermodynamics.
Edit:
The two suggested books have 500 pages of preface, is this necessary or is there a more compact source available?
Best Answer
A definitive volume, one that I learned from during graduate school, is Kerson Huang's (of MIT, emeritus of the Physics Dept.) Statistical Mechanics. The book covers both classical and quantum computations of the partition function and observables from it, as well as thermodynamics, kinetic theory, transport, superfluids, critical phenomena, and the Ising model. Chapters 14 and 15 are devoted to the Ising model.
$J$ can be determined experimentally by knowing, for example, $T_c$. Through a theoretical model including the structure and the species involved you can estimate the value for $J$ through the overlap integrals of the electrons involved.
Here you can read more about exchange interaction, which is the basics behind magnetism (which is a quantum phenomena).
Here is how Chandler does his counting: Take the (square) lattice to be of infinite extent or a finite lattice with periodic boundary conditions in both directions. The total number of edges is equal to $4N/2=2N$ if there are $N$ sites. The ground state corresponds to all spins being in the same state (all up or all down). The ground state energy is $-J$ for every edge and thus one obtains the total energy to be $-2NJ$. For a triangular lattice, the answer will be $-3NJ$.
(converting my comment to an answer following @alemi's suggestion)
Best Answer
A definitive volume, one that I learned from during graduate school, is Kerson Huang's (of MIT, emeritus of the Physics Dept.) Statistical Mechanics. The book covers both classical and quantum computations of the partition function and observables from it, as well as thermodynamics, kinetic theory, transport, superfluids, critical phenomena, and the Ising model. Chapters 14 and 15 are devoted to the Ising model.