Exact Solutions of the Ising Model

University essay from Uppsala universitet/Teoretisk astrofysik

Abstract: This report presents the general Ising model and its basic assumptions. This study aims to, from diagonalization of the Transfer Matrix, obtain the Helmholtz free energy and the exclusion of a phase transition for the one-dimensional Ising model under an external magnetic field. Furthermore from establishing the commutation relations of the Transfer matrices and using the Kramers-Wannier duality one finds the free energy and the presence of a phase transition for the square-lattice Ising model.

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