
OPEN PROBLEMS TREATED BUT NOT PUBLISHED IN ISING THESIS (DISCUSSION)Reinhard Folk (Personal webpage)Institute for Theoretical Physics, University Linz, Austria
In his thesis [1] Ernst Ising solved the problem of a chain of elementarymagnets in an external magnetic field and showed that there is no phasetransition when the magnetic field is set to zero. Goal of the thesis in factwas to proof the existence of the ferromagnetic phase. In order to do so heextended his model for the chain (1) by allowing more than two orientationsof the elementary magnets at one place, (2) by considering two chains (theIsing ladder [2]) and (3) by including nextnearest neighbor interaction inaddition to the nearest neighbor interaction [3]. It should be noted that inorder to calculate the magnetization he had to include into his calculationsof the free energy (partition function) an external magnetic field. It is triedto discuss the results he obtained without knowledge of spin, transfer matrix,duality etc. in comparison with present results.
References:
[1] E. Ising, Beitrag zur Theorie des Ferro und Paramagnetismus. Dissertati on zur Erlangung der Doktorwürde der MathematischNaturwissenschaftlichen Fakultät der Hamburgischen (Universität vorgelegt von Ernst Ising aus Bochum, Hamburg, 1924), see: http://www.icmps.lviv.ua/ising/books.html. 