Orateur
Description
The partition function is a key concept in statistical mechanics: calculating it enables us to determine the physical properties of the system. For the six-vertex model (both rational and trigonometric), imposing certain boundary conditions results in an exact expression. Using the Quantum Inverse Scattering Method, Izergin and Korepin obtained a determinant formula for the partition function of the inhomogeneous lattice and the homogeneous limit for the domain wall boundary conditions (DWBC) on a square lattice. From the latter, Korepin and Zinn-Justin computed the thermodynamic limit to determine certain physical characteristics. Later, Foda and Wheeler developed a model with partial DWBC, modification of the DWBC, to obtain a formula for the partition function on a rectangular lattice.
In the framework of the Modified Algebraic Bethe Ansatz, for the rational case, Belliard, Pimenta and Slavnov derived a formula for general boundary conditions on a rectangular lattice in terms of a modified version of the Izergin determinant. They obtained three different formulae for this determinant: two were derived from previous work, while the third is valid only for a square lattice and resembles the traditional expression for the Izergin determinant.
Together with S. Belliard, we then used the Foda-Wheeler method to extend the last formula to a rectangular lattice, enabling us to obtain a fourth formula for the modified Izergin determinant. Using this final formula, we computed the homogeneous and the thermodynamic limit of the lattice in a same way as Izergin and Korepin, and Korepin and Zinn-Justin, respectively. To conclude, I will present some of the system's physical characteristics that we have computated.
This talk is based on SciPostPhys.20.3.076.