Sprecher
Beschreibung
I review the introduction of the gauge invariant Ising model and my motivation based on my 1971 paper "Duality in generalized Ising Models and Phase Transitions without Local Order Parameter". I start with the exact determination of the critical temperature of the two-dimensional Ising model on the square lattice by Kramers and Wannier 1941 before Onsager gave the exact solution for this model in 1944. The basic idea was that this model was self-dual. Therefore I thought whether something similar could be done for the three-dimensional model. I realized that the dual model is a gauge-invariant model , but it is not self-dual. Increasing the number of dimensions from three to four the gauge-invariant model is self-dual and its critical temperature is the same as for the two-dimensional conventional model. The gauge-invariant model has the property that it has no local order parameter. Non-vanishing correlations are given by products of spins along a loop, called Wilson loop. The expectation value obeys at high temperatures an area law and at low temperatures a perimeter law I mention the dual of the correlations and if time permits some further related work.
