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A<sc>bstract</sc> We study the “three particle coupling”$$ {\Gamma}_{11}^1\left(\xi \right) $$ , in 2dIsing Field Theory in a magnetic field, as the function of the scaling parameterξ:=h/(−m)15/8, wherem∼Tc−Tandh∼Hare scaled deviation from the critical temperature and scaled external field, respectively. The “φ3coupling”$$ {\Gamma}_{11}^1 $$ is defined in terms of the residue of the 2 → 2 elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so thatmis negative. We suggest “standard analyticity”:$$ {\left({\Gamma}_{11}^1\right)}^2 $$ , as the function ofu:=ξ2, is analytic in the whole complexu-plane except for the branch cut from – ∞ to –u0≈ – 0.03585, the latter branching point –u0being associated with the Yang-Lee edge singularity. Under this assumption, the values of$$ {\Gamma}_{11}^1 $$ at any complexuare expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of$$ {\Gamma}_{11}^1 $$ near the Yang-Lee branching point, as well as its known asymptotic atu →+∞. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field.
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A version of Waldhausen's chromatic convergence for TC$TC$
Abstract The map is a weak equivalence.
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- PAR ID:
- 10387929
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 55
- Issue:
- 2
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- p. 945-960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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