Articles dans des revues à comité de lecture
|1D action and partition function for the 2D Ising model with a boundary magnetic field|
|Clusel M., Fortin J.-Y.|
|Journal of Physics A: Mathematical and General 38 (2005) 2849|
|DOI : 10.1088/0305-4470/38/13/003|
|ArXiv : cond-mat/0408657 [PDF]|
In this paper we present an alternative method to that developed by McCoy and Wu to obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system. This method is a generalization of ideas from Plechko presented for the 2D Ising model in zero field, based on the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for a general configuration of the boundary magnetic field. When the magnetic field is homogeneous, we check that our results are in agreement with McCoy and Wu's previous work. This ID action is used to compute in an efficient way the free energy in the special case of inhomogeneous boundary magnetic field. This method is useful to obtain new exact results for interesting boundary problems, such as wetting transitions.