Two-dimensional massive integrable models on a torus

Abstract

The finite-volume thermodynamics of a massive integrable QFT is described in terms of a grand canonical ensemble of loops immersed in a torus and interacting through scattering factors associated with their intersections. The path integral of the loops is evaluated explicitly after decoupling the pairwise interactions by a Hubbard-Stratonovich transformation. The HS fields are holomorphic fields depending on the rapidity and can be expanded in elementary oscillators. The torus partition function is expressed as certain expectation value in the Fock space of these oscillators. In the limit where one of the periods of the torus becomes asymptotically large, the effective field theory becomes mean field type. The mean field describes the infinite-volume thermodynamics which is solved by the Thermodynamical Bethe Ansatz.

Manifest Modular Invariance in the Near-Critical Ising Model

“…In [33], the high-and low-temperature expansions were compared, and it was argued that the sign of D 0,0 in (4) should be negative for T > T c . The D 0,0 piece does not affect most of the discussion in this paper, but the methods of [33] may be useful for developing arguments as in this section for high-vs. low-temperature expansions . 7…”

“…Perhaps most relevant for this paper, a few papers on finite-size effects are reviewed in section 8. A recent paper that relates high-and lowtemperature expansions is [33].…”