1D action and partition function for the 2D Ising model with boundary magnetic field

Abstract

In this article we obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system, by an alternative method to that developed by B. McCoy and T.T. Wu. This method is a generalization of ideas from V.N. Plechko presented for the 2D Ising model in zero field, based on the representation of the Ising model using a Grassmann algebra. In this way, a Gaussian 1D action is obtained for a general configuration of the boundary magnetic field. In the special case where the magnetic field is homogeneous, we check that our results are in agreement with McCoy and Wu's previous work, and we also compute the two point correlation functions on the boundary. We use this correlation function to obtain the exact partition function and the free energy in the special case of an inhomogeneous boundary magnetic field.

References in corpus (8)

• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at $T=T_c$
• Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation
• On Ising Correlation Functions with Boundary Magnetic Field
• Exact Partition Function and Boundary State of 2-D Massive Ising Field Theory with Boundary Magnetic Field
• Logarithmic corrections in the two-dimensional Ising model in a random surface field
• Reflection Scattering Matrix of the Ising Model in a Random Boundary Magnetic Field
• Study of Damage Propagation at the Interface Localization-Delocalization Transition of the Confined Ising Model

Cited by in corpus (5)

• Alternative description of the 2D Blume-Capel model using Grassmann algebra
• Boundary field induced first order transition in the 2D Ising model: Exact study
• Boundary field induced first-order transition in the 2D Ising model: numerical study
• Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques
• Ising model in a boundary magnetic field with random discontinuities