The classical Ising model: A quantum renormalization group approach

Abstract

Proceeding from the equivalence between the d-dimentional classical Ising model and the ( d−1)-dimentional quantum mechanical Ising model in a transverse magnetic field, we study the critical properties of the classical model via the quantum mechanical model. Quantum renormalization group transformations based on the truncation method and the ground state projection operator method are used to calculate the critical exponents. They are found to agree well with the “exact” values.