C. Destri et Hj. Devega, UNIFIED APPROACH TO THERMODYNAMIC BETHE-ANSATZ AND FINITE-SIZE CORRECTIONS FOR LATTICE MODELS AND FIELD-THEORIES, Nuclear physics. B, 438(3), 1995, pp. 413-454
We present a unified approach to the Thermodynamic Bethe Ansatz (TEA)
for magnetic chains and field theories that includes the finite size (
and zero-temperature) calculations for lattice BA models. In all cases
, the free energy follows by quadratures from the solution of a single
nonlinear integral equation (NLIE) (a system of NLIE appears for nest
ed BA). We derive the NLIE for: (a) the six-vertex model with twisted
boundary conditions, (b) the XXZ chain in an external magnetic field h
(z) and (c) the massive Thirring sine-Gordon model (mT-sG) in a period
ic box of size beta = T-1 using the light-cone approach. This NLIE is
solved by iteration in one regime (high T in the XXZ chain and low T i
n the sG-mT model). In the opposite (conformal) regime, the leading be
haviors are obtained in closed form. Higher corrections can be derived
from the Riemann-Hilbert form of the NLIE that we present.