Formfactor perturbation expansions and confinement in the Ising field theory

Details Formfactor perturbation expansions and confinement in the Ising field theory Formfactor perturbation expansions and confinement in the Ising field theory

2009-01-12

arxiv.org/abs/0901.1571v1

J. Phys. A: Vol. 42, 304025 (2009)

Physics

Condensed Matter

Statistical Mechanics

28 pages, 4 figures

Scientific paper

10.1088/1751-8113/42/30/304025

We study the particle spectrum M_n(h) in the two-dimensional ferromagnetic Ising field theory in a weak external magnetic field h. According to Wu and McCoy scenario of the weak confinement, pairs of fermions (domain walls) are coupled into bosonic kink-antikink bound states at small h>0. Fluctuations with more than two fermions also contribute to the wave functions of the compound particles, leading to the multi-fermion corrections to their masses M_n(h) in higher orders in h. We describe a perturbative procedure, which allows to account both multi-fermion fluctuations, and the long-range confining interaction between fermions, and leads to the formfactor expansions for the renormalized parameters of the model. We obtain integral representations for the third-order multi-fermion correction to the mass M_n(h), which arise from the regular correction to the kernel of the Bethe-Salpeter equation.

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