Exact differential renormalization group for the square Ising model
Abstract
We present an exact differential renormalizationgroup method for the square Ising model. This method is analogous to that introduced by Hilhorst et al. for the triangular Ising model. Our approach is based upon the construction of such a renormalization transformation which remains confined to the space of four spatially dependent nearestneighbor interactions. We derive the renormalizationgroup equations in the form of a set of four linear firstorder partial differential equations for the interactions. We obtain a class of solutions of these equations and determine a nontrivial fixed point. The analysis of the flow around the fixed point shows that this fixed point is stable with respect to perturbations within the critical surface and is unstable in the temperaturelike direction. A unique eigenvalue, y_{T}=1, from the eigenvalue equation for the temperature direction is found, in accordance with the exact Onsager solution.
 Publication:

Physical Review B
 Pub Date:
 October 1981
 DOI:
 10.1103/PhysRevB.24.3954
 Bibcode:
 1981PhRvB..24.3954J