Three dimensional Ising model as a non-critical string theory
I will discuss the sign factor problem in the 3D gauge Ising model, present the corresponding fermionic model on random surfaces, which leads to the formulation of non-critical fermionic string theory on the basis of induced Dirac action. I will demonstrate how the sign factor model is linked to ordinary and spin quantum Hall plateau transitions, tying them also to non-critical string theory. Based on the sign-factor model new type of matrix model will be formulated, which allows consideration of any spin chain models on random surfaces. This approach opens the way to cross the c=1 barrier in non-critical string theory.