Abstract
We show that the local magnetization in the massive boundary Ising model on the half-plane with boundary magnetic field satisfies second order linear differential equation whose coefficients are expressed through Painleve function of the III kind.
Highlights
In the work [1] a very simple and elegant derivation of the famous Painleve equations for the spin-spin correlation function in the scaling Ising model with zero magnetic field was given
The approach used in that work was applied in [2] to derive finite volume form factors of spin field in the Ising theory and in [3] to derive the differential equation for spin-spin correlation functions in the Ising theory on a pseudosphere
It turns out to be a second order linear differential equation whose coefficients are expressed through Painleve function of the III kind
Summary
In the work [1] a very simple and elegant derivation of the famous Painleve equations for the spin-spin correlation function in the scaling Ising model with zero magnetic field was given. C. corresponds to the universality class represented by the lattice Ising model with boundary spins all fixed in the same direction The expansion (1)-(3) was first obtained in [9] from lattice model calculations It was shown in [8],[9] that in the cases of ”free” (h = 0) and ”fixed” (h → ±∞) b. Being second order linear differential equation, (16) possesses two linearly independent solutions Their asymptotics as t → ∞ are u1 (t) ∼ 1 and u2 (t) ∼ e(λ−1)t. For λ ≤ 1 more strict condition (17) is required, which follows from form factor expansion (1), (2) Another linearly independent solution in this case has physical meaning. In the rest of the paper we present the details of our derivation of (15), (16)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
