The intrinsic coupling in integrable quantum field theories

Abstract

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed nonperturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XYmodel and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.

High-precision estimate ofg4in the 2D Ising model

“…The aim of this paper is to test this result by using a completely different method. By combining transfer-matrix methods and the exact knowledge of several terms in the scaling function of the free energy of the model we are able to obtain a precision similar to that of [1]. Our result is g * 4 = 14.69735(3), (2) which is in substantial agreement with the estimate of [1].…”

“…In generic 1 In principle, logarithmic terms may also arise from additional resonances due to the fact that y j are integers or differ by integers from y h . They will not be considered here since these contributions either are subleading with respect to those we are interested in or have a form that is already included.…”

“…Recently, in [1], a new interesting approach has been proposed to evaluate this quantity in the case of integrable QFT's. The idea is that for these theories one has direct access to the so called form factors from which the renormalized coupling can be computed.…”

“…The idea is that for these theories one has direct access to the so called form factors from which the renormalized coupling can be computed. In [1] the method was tested in the case of the 2d Ising model. The authors found the remarkably precise estimate g * 4 = 14.6975(1)…”

Lattice artifacts and the running of the coupling constant

“…We have attempted a 1 ln(L) fit to our data but could not obtain a reliable continuum value. (We encountered a similar situation in investigating the renormalized coupling g R in the O(3) model [12]. The case of the O(2) model is simpler to handle because the theory predicts both the continuum value and the leading correction [11].)…”